Mbappe was fouled and confidently put his spot kick to the right of goalkeeper Rémy Descamps in the 78th minute, then pointed at a pitchside television camera and smiled before vigorously clenching his fist.
It took his league-leading tally to 21 and his season's haul to 32 in 31 games. After the final whistle he took off his jersey and gave it to PSG's travelling fans.
He was put on the bench by coach Luis Enrique, two days after finally telling PSG he's leaving at the end of the season. He came on in the 61st just after Lucas Hernández scored with a shot that deflected and looped over Descamps.
Enrique may well have been resting Mbappé since he has been nursing a sore left ankle recently and also sat out last Sunday's home game against Lille.
Left winger Bradley Barcola forced a save from Descamps 10 minutes into a tight first half. Near the end of it, Nantes twice went close following quick counterattacks and had a goal from defender Nicolas Pallois disallowed for offside.
Pallois forced PSG goalkeeper Gianluigi Donnarumma to tip over with a dipping shot from 25 metres early in the second half, and lively forward Mostafa Mohamed drew another save from him with 10 minutes remaining.
In an earlier game, Canada striker Jonathan David showed he is back in the scoring groove by grabbing a hat trick as Lille beat Le Havre 3-0 to move up to third place.
After a quiet start to the season, David has scored six times in the past three homes games to move onto 11 league goals overall, good for second in the scoring charts behind Mbappé.
David is Lille's record signing, costing the northern club 27 million euros in 2020. He is expected to join a bigger team next season.
He pounced from close range in the 14th, netted moments before halftime after being set up by midfielder Angel Gomes, and followed up his own saved penalty in the 49th.
Lille are ahead on goal difference from Monaco, who play on Sunday.
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