The hosts only had a Dimitrios Nikolaou own goal to show for their first-half dominance before Olympiacos were handed a glimmer of hope in the closing stages of the opening 45 minutes when Gerard Pique was shown a second yellow card.
However, Messi's milestone strike and Lucas Digne's first Champions League goal for the club ensured that they remain perfect in Group D, despite Nikolaou going some way towards redeeming himself with a late consolation.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute updates below.
This game pits top versus bottom in Group D against each other, with Barcelona able to move a big step towards reaching the last 16 should they make it three wins from three tonight whereas Olympiacos realistically need to pick up something if they are to keep their own slim hopes alive.
Before we take a closer look at both camps, though, let's first check out the team news for tonight...
Well, the headline news unsurprisingly comes from the Barcelona camp as Gerard Deulofeu returns to the fold for the home side, which should in turn bring with it a switch back to the 4-3-3 formation. Barca have mainly played with more of a 4-4-2 since losing Ousmane Dembele to a long-term injury, but they clearly feel that they can afford to be a little more attacking this evening.
Messi, for his part, has also been named in the three-man shortlist for FIFA's The Best awards, and he will find out whether he has scooped that prize in just five days' time. He has certainly done his best to win it so far this season, scoring 17 goals in 16 games for club and country in 2017-18.
Messi has scored in each of Barcelona's last three games against Greek opposition too, and Olympiacos must be concerned about their chances with the Argentine in such good form. Suarez, meanwhile, got a late equaliser against Atletico Madrid at the weekend to get back on the goal trail himself.
Andre Gomes, who was a surprise inclusion from the start against Atletico, is among those to drop to the bench tonight amid rumours that Messi and Suarez questioned his selection at the weekend, with Paulinho replacing him in the starting XI.
Semedo is just one booking away from suspension which is perhaps the reason behind his exclusion, but Alba does not even make the bench as he is given the night off. Semedo and Alba are also the only two changes from the matchday two win over Sporting Lisbon, incidentally.
It looks like Olympiacos will play with something similar to a 4-3-3 formation tonight, although in practice is likely to be more like a 4-5-1 system. Odjidja-Ofoe looks like being the furthest forward from the teamsheet submitted, although we will wait to see if that is actually the case.
Cisse, Figueiras, Pardo, Fortounis, Seba and Ansarifard all drop out of the team from Saturday's match, the latter of whom can feel particularly hard done by having scored twice to help Olympiacos to victory against Panionios.
The Spaniard joined the Barcelona academy at the age of 14 and spent three years in their B side before making his one and only senior appearance for the club in a 1-1 draw with Deportivo La Coruna on the final day of the 2008-09 season. Botia went on to place for Sporting Gijon, Sevilla and Elche in Spain, although he failed to win any of his nine matches against Barca in that time.
A turbulent summer off the field, during which Barca lost their manager Luis Enrique and then the £200m man Neymar, looked to be creeping into the new season when they began the campaign with back-to-back defeats at the hands of fierce rivals Real Madrid in the Super Cup, but since then everything has gone very well for the new man in charge Ernesto Valverde.
Barca's first ever visit to the Wanda Metropolitano was never going to be easy, and sure enough they saw their 100% La Liga record ended by Diego Simeone's side, but even though they needed a late goal from Suarez to earn a point, Barca's performance still garnered praise.
There is still a long way to go, of course, but Barcelona look to be in fine form and do not drop many points over the course of a campaign, so a five-point gap is already a big ask for Madrid to make up. Could Ernesto Valverde wrest the league and Champions League crowns off Real Madrid in his first season at the Camp Nou?
Of course, the Greek Super League is not quite the same challenge as La Liga, but during his time with Olympiacos Valverde helped the club to three league titles and two Greek Cups, so his time in charge will be fondly remembered by tonight's visiting fans.
Juventus, who knocked Barcelona out of the tournament last season, were swept aside 3-0 in their opening game here at the Camp Nou and, while things were not quite as straightforward on matchday two when Barca needed an own goal to scrape past Sporting Lisbon, it is still maximum points and no goals conceded for Barca so far in this season's competition.
At home it has been particularly impressive, with only one goal conceded from their last five matches - all of which have ended in Barcelona victories, scoring 19 goals in the process at an average of just under four per game.
It is a similar story in the Champions League, where Barca are unbeaten in their last 22 outings on home turf, winning a whopping 20 of those. You have to go back to May 2013, when they lost 3-0 at home to Bayern Munich in the semi-finals, for their last European defeat at the Camp Nou, and that is their only loss here in their last 45 - a run which stretches back just under eight years.
The dominant force in Greek football, with seven title wins on the bounce including last season, Olympiacos have made a stuttering start to their campaign both domestically and in Europe, to such an extent that their main focus may already be turning to the Super League rather than salvaging anything from this difficult Champions League group.
That is not to say that Olympiacos's hopes of an eighth straight title are over yet, though - they are still just four points adrift of leaders PAOK and will fancy their chances to overcoming their poor form so far.
Three of those losses came on the bounce too, which made for the club's worst run of form since February 2009 before they finally stopped the rot with a last-gasp 4-3 win over Panionios having earlier squandered their two-goal lead by conceding twice in the final 10 minutes.
Lemonis's side have been fine going forward domestically this term, scoring more goals than any other side in the Greek Super League, but it is at the other end where their main problems have come. They the second-worst defensive record in the league, ahead of only bottom-placed Larissa, and are without a clean sheet in any of their last eight games across all competitions.
Two late goals from Pardo saw Olympiacos make the score more respectable as they fell to a 3-2 home defeat, but it could have been a lot worse than that, with Sporting Lisbon missing plenty more chances in the opening 45 minutes. Olympiacos were better against Juventus last time out, but they still succumbed to a 2-0 defeat and things will not get any easier tonight.
That 3-2 defeat at home to Sporting Lisbon on matchday one could well scupper those chances, though, and Olympiacos will likely need to pick up unexpected points against either of the big boys if they are to claw themselves off bottom spot in Group D.
Olympiacos's last group stage campaign before this season also saw them win two of their three away games - including a 3-2 triumph over Arsenal at the Emirates - although they did also lose 4-0 to Bayern Munich at the Allianz Arena.
I am struggling to see anything other than a Barcelona win in this one. The hosts are in fine form and are coming up against an inferior team in pretty poor form themselves. It should be routine for Barca, who have the quality to pick through Olympiacos even if the visitors try to sit back and frustrate the hosts.
SPORTS MOLE SAYS: Barcelona 4-0 Olympiacos
Barca do have plenty of experience against other Greek opposition, though, and the omens are good for them having won nine and lost just two of their 12 previous meetings with Super League sides. That includes wins in each of their last three games - all of which came against Panathinaikos and which saw them score 13 goals in total, with Messi on the scoresheet in each of them.
In contrast, Olympiacos has never won in 14 previous visits to Spain, losing 12 of those and only coming away with so much as a draw on two occasions.
You have to go back 12 years - to the 2004-05 Champions League group stages - for the last time Olympiacos avoided defeat on Spanish soil, earning a 0-0 draw with Deportivo La Coruna on that occasion.
BARCELONA STARTING XI: Ter Stegen; Roberto, Pique, Umtiti, Digne; Paulinho, Busquets, Iniesta; Deulofeu, Suarez, Messi
OLYMPIACOS STARTING XI: Proto; Elabdellaoui, Botia, Nikolau, Koutris; Gillet, Romao, Zdjelar, Carcela-Gonzalez, Androutsos; Odjidja-Ofoe
Elsewhere, Chelsea have broken the deadlock against Roma through David Luiz.
With the conditions and the joy Barca have got down the flanks, there was always a danger of this happening. Deulofeu stays onside and volleys the ball across the box which Nikolaou has to try to clear. However, his attempted clearance skims off his shin and past a helpless Proto.
Elsewhere, Joshua Kimmich has doubled Bayern Munich's lead against Celtic, while Basel are not ahead against CSKA Moscow in Manchester United's group.
...but Roma quickly get one back through Aleksandar Kolarov! It's 2-1 in West London now!
It initially looks like Barca have finally got their second as Deulofeu's drilled low strike was only parried into the path of Pique, who turned the ball home from close range. However, the Scottish officials quickly disallow the goal and suddenly brandish another yellow card for the already-booked Pique.
The replay shows that Pique was not offside, but he put the ball in with his hand and that was the reason for disallowing it and giving the Spain international his marching orders.
Barcelona could - and should - be further ahead at the interval, but as things stand they have just the one-goal advantage despite dominating with 70% possession and 13 shots to Olympiacos's 1.
There was always the danger of that happening due to the rain and the amount of crosses Barcelona were getting into the box, with Deulofeu - who has been the standout player so far - providing the cross that led to the own goal.
Luis Suarez has squandered another glorious one when he was denied one on one, while Deulofeu, Messi and Busquets have also had sights of goal.
The first yellow was shown for a cynical tug on Odjidja-Ofoe, but it was the second that proved most costly. Deulofeu's low strike was parried into the path of Pique, who bundled it over the line from close range. However, rather than being awarded the goal, Pique was given his marching orders after the Scottish officials has spotted that his turned the ball home with his hand.
It is not the very best of his career, but it is good enough to make it past the keeper, who got a hand to it but could not keep it out. Messi gets it over the wall and, while it is not right in the corner, the keeper just cannot claw it away.
The Argentine maestro is the creator for this goal, skipping past one marker with his dazzling footwork before pulling the ball back into the area. It is just too far in front of Paulinho and Iniesta, but Digne is there to drill home his first Barca goal in this competition.
Barcelona old boy Neymar has joined Mbappe and Cavani on the scoresheet to give PSG a 3-0 lead over Anderlecht, while Roma have come from two down to level things up against Chelsea.
Despite their utter dominance in the first half they could only muster an own goal to take the lead before Gerard Pique was shown a red card, but second-half strikes from Lionel Messi and Lucas Digne finally took the game away from the visitors. Olympiacos did grab a stoppage-time consolation through Dimitrios Nikolaou - who had scored the earlier own goal - but they were comfortably second best tonight.
Thanks you very much for joining Sports Mole for tonight's match as Barcelona move one step closer to qualifying for the last 16 with a 3-1 win over Olympiacos despite being reduced to 10 men in the first half. I will leave you with our match report, and be sure to stick around for reaction too.
From me, though, it is goodbye for now!