The 23-year-old made it seven goals in five Ligue 1 games so far this season with goals either side of half time, before Nuno Mendes capped off the scoring for the champions.
Nantes had earlier seen Fabio shown a straight red card as they rarely threatened to get anything from a game which leaves PSG on 16 points from a possible 18 so far this term - level with Marseille at the top of the table.
The two sides traded chances before the opener, with Samuel Moutoussamy and Mostafa Mohamed enjoying sights of goals for the hosts and Marquinhos and Danilo Pereira doing the same for PSG.
It was inevitably Mbappe who broke the deadlock, though, firing an unstoppable strike into the top corner after being found by Messi.
Any hopes of Nantes getting back into the match were then severely hampered by Fabio seeing red for a high challenge, leaving the home side to see out more than an hour with 10 men.
Nantes held out until 10 minutes into the second half, when Mbappe doubled his personal tally by converting Messi's pass from close range, having seen his own attempt to set up Messi temporarily thwarted by Nicolas Pallois.
The goal was initially ruled out for offside, but a lengthy VAR review ruled that Mbappe was indeed onside earlier in the move.
Mbappe's hat-trick chances were ended when he was taken off for Neymar, and the Brazilian almost got his own name on the scoresheet in the buildup to the third when his effort came back off the woodwork and rebounded to Mendes, who finished it off.
Messi, who now boasts three goals and six assists in six games this season, was denied a fourth for his side on the night late on, but by that stage the result was already sewn up as PSG extended their unbeaten start to the campaign.