Producing the last goal of Saturday's match at the Parc des Princes gave 24-year-old Mbappe his 201st goal for PSG and eclipsed Edinson Cavani's club record.
The third consecutive win moved PSG 11 points clear at the top of the standings, but it was marred by the replacement of Marquinhos late in the match.
Marquinhos was substituted with 15 minutes left, clutching his back in pain. He's in doubt for when PSG travel to Bayern Munich on Wednesday for the second leg of their Champions League round-of-16 tie. Bayern lead 1-0 from the first leg.
Mbappe missed several chances for the milestone goal in the last five minutes.
Then he collected a pass from Timothee Pembele, quickly turned toward the goal and fired home with a left-footed shot.
PSG fans chanted Mbappe's name amid fireworks and he was later presented with a trophy marking the achievement.
"I was still a young player when I arrived here. I've learned a lot here," Mbappe said after his 247th game with PSG.
"I play to write history, and I always said that I want to do it here, in France, in its capital city. . . . It's a personal achievement but I also came here for collective achievements."
PSG led 2-0 after 16 minutes and looked set for a comfortable evening, but for the second time in a row at home, Christophe Galtier's players wasted a two-goal lead before they prevailed.
Following a 3-0 win at second-placed Marseille last weekend, PSG returned home full of confidence against Nantes and quickly took control with a fluid passing game.
Lionel Messi broke the deadlock with a low shot in the 11th minute after connecting with a cross from Nuno Mendes. PSG doubled the lead when Jaouen Hadjam, under pressure from Nordi Mukiele, beat his own goalkeeper with a poor clearance attempt.
Nantes needed an individual moment of brilliance from Ludovic Blas to pull one back. After being set up down the left, the attacking midfielder took Gianluigi Donnarumma by surprise with a shot from a tight angle in the 30th.
Ignatius Ganago leveled in the 37th after a corner when the ball went in off his back.
Nantes defended well and played boldly after the interval but PSG found an edge at the hour mark. Danilo Pereira headed home from Mbappe's cross, then the France striker beat Cavani's record to seize the limelight.
Canada forward Jonathan David snatched a second-half equaliser for Lille to finish 1-1 at bitter rival Lens in the northern derby.
David's 16th goal of the season - second only to Mbappe - came in the second half after goalkeeper Brice Samba denied consecutive efforts from Jonathan Bamba and Remy Cabella in the box.
With 50 goals in all competitions for Lille in less than three seasons, David moved level with Eden Hazard as Lille's top scorer in the 21st century.
Lens moved up to third place, one point above Monaco, which plays on Sunday. Lille stood sixth, six points behind Lens.
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