The teams looked like going into the break all square following an even first half before Lionel Messi scored in the final minute of normal time to give the hosts the lead.
Messi's influence grew further in the second half too, and the Argentine was instrumental in creating a second for Ivan Rakitic before putting the seal on the victory himself.
Find out how all of the action unfolded courtesy of Sports Mole's minute-by-minute coverage below.
It is a game which would grace the final - as it did as recently as 2015 - as Barcelona host Juventus at the Camp Nou in their opening Group D fixture. These two sides should occupy the qualifying spots once all is said and done in this group, but the main question is what order they will come in, and tonight's match could have a big bearing on that. Just last season this fixture graced the quarter-finals, and it is sure to be another memorable affair as two of Europe's biggest clubs clash on matchday one.
Before we take a closer look, though, let's first check out the team news...
Well, the headline as far as the hosts are concerned is a full debut for Ousmane Dembele, who came off the bench during the 5-0 win over Espanyol at the weekend and had an impact by assisting Suarez's goal in the Catalan derby. The youngster has plenty to prove before he can fill the sizeable hole left by Neymar's departure, but Barca clearly have great faith in him and he replaces Gerard Deulofeu in the starting XI tonight.
Big night for the France international!
Not that either need to be made more devastating. Suarez has been quick to get back on the goal trail following a spell out through injury, while Messi netted a hat-trick against Espanyol - his 42nd of his career and 38th for Barcelona - to make it five goals in his last two games.
It is still a very good defensive unit, but certainly not as strong as it was when the two teams last met in April.
Even if Barcelona are able to keep Dybala quiet then they must then also deal with Douglas Costa and Gonzalo Higuain, the latter of whom knows Barca well from his time with Real Madrid.
Their journey starts here tonight, though, and Barcelona's home advantage just about makes them favourites in this battle of the European giants. Barca have the greater pedigree in this competition too, although in recent seasons it is Juve who have outperformed the Catalan outfit. Indeed, Barca have been knocked out in the quarter-finals of the last two Champions League seasons, which is a disappointing return for a club of their stature.
They have gone on to win their group a record 18 times too, including every year for the past decade - last failing to do so in 2006-07 when they went into the campaign as holders.
Valverde has not been at a club like Barca in that time, of course, but when compared to Allegri's record of reached the knockout rounds in each of his seven years as a Champions League manager, there is a discrepancy in the dugout tonight.
Upsetting the food chain like PSG certainly hasn't gone down well in Spain, and having lost Neymar the Catalan giants then lost back-to-back matches against El Clasico rivals Real Madrid in the Spanish Super Cup before missing out on Philippe Coutinho on deadline day.
Barca have won all three of their opening La Liga fixtures and currently sit top of the table as one of only two teams with a 100% record. Barca are also one of only two teams yet to concede in La Liga this season, scoring nine goals without reply in their opening three fixtures.
Perhaps more importantly, though, they already find themselves four points clear of Real Madrid and Atletico Madrid.
Only one team has managed to stop them scoring in their last 23 home games in all competitions, and that just so happens to be Juventus in the quarter-final here last season.
At home, though, they have been imperious. They are unbeaten in their last 21 Champions League games at the Camp Nou, winning 19 of those in a run which stretches all the way back to May 2013. Indeed, former manager Luis Enrique only failed to win one of his Champions League home games during his time in charge of the club, but once again that was the 0-0 draw with Juve here last term.
Having utterly dominated Italian football for the past six seasons - winning Serie A each year and the double in each of the last three years - Juve somewhat surprisingly made it all the way to the final in 2015. By Allegri's own admission it came earlier than planned and they weren't fully expecting to beat Barcelona, but last season's run to the final was all the more predictable.
Juve may have to duke it out for top spot with Barcelona, but with Olympiacos and Sporting Lisbon their other Group D opponents to come, there should be much for either the Spanish or Italian giants to worry about.
Three wins from three has put them above fell 100%ers Napoli and Inter Milan as they go in search of an unprecedented seventh consecutive title.
Juve had conceded just three goals all tournament going into the final, but they proceeded to conceded four in one night to condemn themselves to another defeat.
Whichever way the result goes tonight, we should be in for a treat as two of the best sides in world football do battle, but the home advantage could prove vital for Barca. Juventus managed to hold them to a goalless draw here on their last visit when Barca still had Neymar, but the circumstances are different tonight. Add to that the fact that Juve are without arguably their best defender and I have to back the hosts here.
Sports Mole says: 2-1
All of those goals came in Turin, with Dybala notching a brace before Chiellini added a third to take the tie further away from Barcelona, who were unable to produce another miraculous second-leg comeback as they drew 0-0 here in April.
That remains Barca's solitary win over Juve in their last six competition meetings, including another quarter-final in 2002-03 in which Juve prevailed.
BARCELONA STARTING XI: Ter Stegen; Semedo, Pique, Umtiti, Alba; Busquets, Rakitic, Iniesta; Dembele, Suarez, Messi
JUVENTUS STARTING XI: Buffon; De Sciglio, Benatia, Barzagli, Sandro; Pjanić, Matuidi, Bentancur; Dybala, Douglas Costa, Higuain
The referee didn't see it and awards a goal kick, but that was a crucial touch from Ter Stegen.
Things don't look quite as rosy for Anderlecht, who are now down to 10 men and 1-0 down against Bayern Munich at the Allianz Arena.
Perhaps Dembele had watched the incident with Sadio Mane and Emerson on Saturday and decided against risking the red card.
This one remains very finely poised.
Messi collects the ball in a deep position and opts against the easy pass out to Alba in favour of sneaking a clever one into the feet of Suarez. Suarez instinctively plays the return ball, and Messi then steers his accurate finish into the bottom far corner.
It is the first time that Messi has ever scored past Buffon, and there was nothing the goalkeeper could do there. Brilliant football from the Barcelona duo.
The hosts have seen almost two-thirds of the possession, but Juventus have had plenty of sights of goal themselves and the half-time stats show that they have actually had more shots than Barcelona. This one is far from over, though, and a fascinating 45 minutes await.
The Barca talisman had been kept quiet by a disciplined Juventus performance, but he only needs a half-chance to make the opposition pay and he made the most of it when it came. Messi collected the ball just inside the Juve half and drove forward before exchanging passes with Suarez and tucking a pinpoint finish into the bottom far corner.
Big, big chance, and you don't get too many of them against Barca!
An element of fortune about that one for Juventus, especially as the referee pointed for a goal kick despite the ball clearly coming off Buffon last.
The five-time Ballon d'Or winner floats out to the right flank this time and darts in behind Sandro, racing into the box before squeezing a low pass past Buffon towards Suarez. Sturaro gets there first to clear the ball almost off his own line, but it goes straight to Rakitic, who is left with a simple finish. Messi is beginning to dazzle here.
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The Argentine has been afforded more space in this second half and he collects a pass around 25 yards from goal this time. It is obvious what he is going to do, but stopping it is a completely different story as he cuts inside onto his left, beats a couple more defenders and fires his finish into the bottom corner, leaving Buffon no chance.
Game over, and Messi is now on yet another hat-trick.
Alba is the man offside as he races down the left flank before playing a low ball into the box which Buffon spills right at the feet of Suarez. It is howler from the veteran keeper, and Suarez duly punishes him, but Buffon's blushes are spared by the flag.
In the end it was all rather comfortable for the hosts as they ran out 3-0 winners, with Lionel Messi once again the star of the show with two goals either side of a Rakitic strike which he was also heavily involved in. It was actually an even match for the opening 45 minutes, but Messi broke the deadlock on the stroke of half time and then ran the second half to take the game beyond the Italian champions.