The match was a repeat of last season's quarter-final which Juve won 3-0 on aggregate, but it was Barcelona who prevailed by that scoreline on matchday one as Messi continued his inspired early-season form.
The 30-year-old opened the scoring on the stroke of half time before creating one for Ivan Rakitic and scoring another of his own as Barca laid down an early marker in this season's competition.
Barcelona handed a full debut to summer signing Ousmane Dembele in what was Ernesto Valverde's first Champions League match in charge of the club, while Juventus welcomed back the likes of Gianluigi Buffon, Paulo Dybala and Andrea Barzagli into their starting lineup.
The visitors were still missing a number of key players, but it did not stop them making a bright start to the match and they almost took the lead in spectacular fashion from an unlikely source after just six minutes when Mattia De Sciglio - who failed to score in 133 appearances for AC Milan - marked his first Juventus start with a 25-yard drive which needed to be tipped past the post.
Dybala, who scored twice as Juve eliminated Barcelona in the quarters last season, also came close in the opening 10 minutes when his effort at the end of a counter-attack called Marc-Andre Ter Stegen into action, and the Barcelona keeper was busy again shortly afterwards when he got down well to deny Miralem Pjanic.
Buffon didn't have a serious save to make until the 20th minute, but the veteran was alert when he was finally forced into action, tipping over Luis Suarez's powerful first-time drive after a Messi free kick had hit the wall.
Juventus did an effective job of keeping Barcelona at bay for the majority of the first half, but they almost gifted the hosts an opening goal with less than 10 minutes remaining of the half when De Sciglio's loose pass was picked off by Dembele inside the area, and it took a last-ditch saving challenge to prevent the France international from getting a shot away.
The opening goal did arrive on the stroke of half time, though, as Messi - who had been kept quiet for the most part up to that point - suddenly burst into life by driving forward before playing a one-two with Suarez and rolling an accurate finish into the bottom corner.
It was Messi's sixth goal in his last three games off the back of his hat-trick at the weekend, but the first time that he had ever managed to score past Buffon in his illustrious career.
It would not be the Argentine's last of the night, though, and his growing influence on the game allowed Barcelona to take a firmer grip in the second half.
Things may have been different had his international teammate Dybala not squandered Juve's clearest chance of the night moments after the restart, blazing the ball over the crossbar when he should have at least hit the target after Gerard Pique's interception had fallen kindly for him.
It was the Messi show from that point on, though, and the five-time Ballon d'Or winner almost doubled his personal tally for the evening in the 52nd minute when his powerful 25-yard drive struck the post before bouncing back off the beaten Buffon and behind.
The Argentine maestro turned provider for the second goal when he darted in behind the defence down the right channel before playing a low pass into the middle which Stefano Sturaro needed to deal with on the line. The Juventus sub's clearance only went as far as Rakitic, though, and the Croatian was left with an easy finish on the follow-up.
Buffon was then called into action to deny a free kick from Messi before Suarez almost got in on the act with a near-post effort that rose narrowly over the crossbar.
The third goal did arrive with a little over 20 minutes remaining, though, as Messi took his tally of Champions League goals up to 96 - including 59 in 58 group games - by cutting inside his marker and beating a helpless Buffon from the edge of the box.
The hosts thought they had a fourth goal 10 minutes later when the Juve goalkeeper uncharacteristically spilled the ball at the feet of Suarez in the box and was duly punished, but the linesman's flag spared Buffon's blushes.
Juventus enjoyed a brief revival in the final 10 minutes as Dybala drew a smart save from Ter Stegen before Mehdi Benatia saw his header from the resulting corner cleared off the line by Pique, but the match was over as a contest by that stage and Barcelona comfortably held on for the win.
Barca, who immediately rise to the top of Group D, have now won their last four games in all competitions without conceding a goal, whereas Juventus have already lost more Champions League away games this season than they did during their run to the final last term.