Lionel Messi opened the scoring from the penalty spot, but that was as good as it got for Ronald Koeman's side as Mbappe took over to evoke memories of recent defeats to Bayern Munich, Liverpool and Roma.
The French striker equalised before the break and then gave PSG the lead in the 65th minute. Moise Kean headed in the third for Mauricio Pochettino's side before Mbappe completed his hat trick on the break late on.
Gerard Pique is back from injury earlier than expected. Less than three months after damaging knee ligaments, he started against PSG. It didn't make much difference, but having him available again should be good in the long term.
It should be positive that Barca have the second leg to turn the tie around, but in the wake of this defeat that doesn't feel very likely. Things could get ugly if they leave spaces looking for a way back into the game.
PSG took full advantage of the space afforded to them at Camp Nou and, even though Barca have been on a good run domestically in winning seven league games in a row, this was a reality check. There was a lingering doubt that they hadn't yet beaten anyone of note and, once again, coming up against a better side they were easily beaten. It's back to the drawing board for Koeman's side, who looked slower and weaker than their opposition.
In the long term, another humiliating Champions League exit could be the final straw for Messi, who's out of contract at the end of the season and likely to leave if he doesn't believe Barca can compete at the top level anymore.
Manager rating out of 10
4 -- Koeman's decision to throw Pique straight back into the side was one of a coach who trusts individuals above his system. And as his system was being taken apart in the early stages of the second half, he did nothing to rectify it, watching Mbappe get the better of Sergino Dest repeatedly.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
DF Sergino Dest, 4 -- Struggled with the strength and pace of Mbappe all night to the point that Koeman replaced him with Oscar Mingueza in the second half.
DF Gerard Pique, 5 -- Lasted 78 minutes on a surprise early return from knee ligament damage and was vocal at the back, barking instructions. However, he was slightly off the pace and the image of him diving to pull back Mbappe summed up the match.
DF Clement Lenglet, 5 -- Didn't do anything especially wrong, but that in itself is worrying. Simply wasn't good enough to deal with Mbappe up close and was oblivious to the unmarked Kean behind him for the third goal.
DF Jordi Alba, 5 -- Struggled with the threat posed by Kean on the right and wasn't able to have an effect in attack.
MF Sergio Busquets, 5 -- Had his good moments, but left too much space in front of the back four and gave the ball away too often high up the pitch, leaving Barca exposed.
MF Pedri, 6 -- Involved in some good moments, feeding one great pass to set up a Antoine Griezmann chance, but also caught on the ball too often. Managed to make up for one ball loss with a goal-line clearance.
FW Ousmane Dembele, 5 -- Missed a great chance to make it 2-0 minutes after Messi's penalties and switched off in his defensive duties, allowing Kurzawa to create the PSG equaliser and then, minutes later, leaving the same player unmarked for a free shot on goal.
FW Lionel Messi, 6 -- As hard as he tried, he couldn't take control of the game as he would have liked. Took his penalty well and created a couple of chances for his teammates, but was denied space in the final third by PSG's impressive game plan.
FW Antoine Griezmann, 6 -- Missed some good chances, although none were easy. Was denied by Keylor Navas early in the game and shot wide on the break after carrying the ball 40 yards. Almost caught Navas out late in the game when blocking a pass from the goalkeeper, only to see the ball drop agonisingly wide.
DF Oscar Mingueza, 6 -- Replaced Dest with the aim of stopping Mbappe, which is perhaps an impossible task.
MF Riqui Puig, NR -- Thrown on when Barca were already on the ropes.
MF Miralem Pjanic, NR -- Worked hard in his short cameo but, as with Puig, his time came too late.
FW Francisco Trinaco, NR -- Made one really impressive surging run forward, but it came to nothing.
FW Martin Braithwaite, NR -- Had a couple of half-chances late on, but PSG defended his presence in the box well.