French international Mbappe was left out of the starting line-up by coach Christophe Galtier with one eye on Wednesday's Champions League clash at Benfica.
That is one of 11 fixtures the French champions face in the six weeks leading up to the World Cup.
Mbappe was replaced by 20-year-old Hugo Ekitike, who was making his first start for PSG.
However, it was fellow superstar Lionel Messi who grabbed the early attention when he gave PSG a 29th-minute lead with a sumptuous, curling free-kick which sailed over the Nice wall and past goalkeeper Kasper Schmeichel.
Gaetan Laborde levelled for Nice, who were coached by Galtier until this season, in the 47th minute after PSG got into a terrible defensive tangle.
Mbappe was summoned from the bench on the hour mark and struck the winner with seven minutes left after Nice attempted and failed to play the ball out of defence.
The goal was Mbappe's eighth of the league season and took him level with teammate Neymar at the top of the scoring charts.
PSG have a two-point lead over Marseille who defeated Angers 3-0 on Friday.