Messi, regarded as one of the greatest players of all time, was then upstaged on his own turf by France World Cup winner Mbappe as PSG ruthlessly exposed the hosts.
Mbappe danced past Clement Lenglet and smashed in the equaliser before stroking home from 10 yards to turn the game around.
On-loan Everton striker Moise Kean continued his resurgence by heading in unchallenged at the far post to put the Ligue 1 champions in control of the tie.
With Barca looking to pull a goal back, they were caught on the counter-attack and Mbappe curled in the goal of the night with his third.
The second leg takes place on 20 March in Paris, by which time PSG hope to have Neymar back from a thigh injury to face his former side.
Magnificent Mbappe steals the show
Champions League meetings between European heavyweights can often be tense, nervy encounters but this was a thrilling end-to-end clash which will live long in the memory as Mbappe took home the match ball.
The 22-year-old fell agonisingly short last season when they were beaten in the final by Bayern Munich, and the Ligue 1 champions will take some stopping again under Mauricio Pochettino.
Sacked by Tottenham in November 2019, just five months after reaching the final of this competition, Pochettino looks to be moulding a side that will be considered strong contenders led by the brilliant Mbappe.
He had netted just one goal in nine knockout games for PSG before this game, but reversed that statistic in cold-blooded fashion.
The former Monaco forward became only the third player, after Faustino Asprilla and Andrei Shevchenko, to score a Champions League hat-trick against Barcelona.
He took his first majestically, trapping Marco Verratti’s delightful flick before ghosting past compatriot Lenglet and firing an unstoppable finish past Marc-Andre Ter Stegen.
The second was a poacher’s finish from 10 yards after the Barca goalkeeper parried the ball back into the danger area but he saved his best until last, curling in a first-time finish to stun the home side.
They should have had more but for Ter Stegen, who made superb saves to deny Layvin Kurzawa and Kean twice, but the Italian striker did find the net with a header on 70 minutes.
Though in command, PSG will know the tie is not over having been on the wrong end of a Barcelona comeback when the sides met at this stage in 2016-17, Luis Enrique’s men turning around a 4-0 deficit to win the return leg 6-1 with three late goals.
Dembele’s miss proves pivotal
Riddled with debt and uncertainty surrounding the future of star man Messi, as well as presidential elections coming up next month, Barcelona were well beaten by their more sprightly and effervescent opponents.
Messi gave them the perfect start by converting a penalty after Frenkie de Jong was tripped in the box but it was all downhill thereafter.
They will look to a bad miss from Ousmane Dembele at 1-0, striking a weak effort straight at Keylor Navas from 10 yards out, as the turning point in the game.
Had that gone in it may well have been a tighter scoreline, and with Antoine Griezmann also missing from close range and shooting wide from the edge of the box, Ronald Koeman’s men were heavily punished at the other end.
PSG continue scoring run on the road – the stats
- In what is their 151st home match in the European Cup/Champions League, Barcelona have lost consecutive matches for the very first time.
- Barcelona have played 278 home matches in all European competitions and have lost by a 3+ goal margin only six times – the past two occasions have come in successive games at the Nou Camp (3-0 v Juventus, 4-1 v PSG).
- Paris St-Germain became just the second French side to beat Barcelona at home after Metz also won 4-1 in the 1984-85 Cup Winners’ Cup.
- PSG have scored in each of their past 20 away matches in the Champions League, a run dating back to September 2016. In the competition’s history, only Real Madrid have had a longer run – 22 games from 2010-2014.
- Of players with 20 or more goals in the Champions League, PSG’s Kylian Mbappe has netted the highest proportion in away matches (71% – 17/24).
- Lionel Messi’s opener was his 20th goal of the season for Barcelona in all competitions; it’s the 13th consecutive campaign he’s scored 20+ goals for the club.
- Messi has scored in the Champions League in each calendar year since 2005. This run of at least one goal in 17 consecutive years is the joint-longest run in the competition’s history alongside Raul (1995-2011)