He had to wait until the 92nd minute but was clinical as he turned to finish left-footed and go clear of Edinson Cavani at the top of the PSG goal list.
The France forward, who turned 24 in December, has established himself as a footballing superstar.
He has played at two World Cup finals, winning the trophy in 2018 and earning the Golden Boot as top scorer in 2022.
Mbappe, who also won the 2021 Nations League with his country, scored a hat-trick in December’s World Cup final against Argentina, which France lost on penalties after a 3-3 draw.
This season, the forward has now scored 30 goals and made eight assists – taking his total to 85 for the club in 247 games.
PSG went 2-0 up at the Parc des Princes with Lionel Messi opening the scoring before Jaouen Hadjam’s own goal.
However, Nantes came back to level before half-time thanks to goals from Ludovic Blas and Ignatius Ganago, with PSG goalkeeper Gianluigi Donnarumma caught out at his near post for the first and making a fumble that led to the second.
Mbappe crossed for Danilo Pereira to head the home side back in front on the hour mark before his crowning moment came late in the game.