Mbappe opened the scoring before the break and joined Alessandro Florenzi and Pablo Sarabia in netting inside the final 12 minutes to put PSG on 15 points from seven games, four days before hosting United at the Parc des Princes.
They lead Stade Rennes on goal difference after the Brittany side were held to a 1-1 draw at bottom club Dijon.
Nimes, who are 13th on eight points, were reduced to 10 men after 12 minutes when Loick Landre was red carded.
PSG lost Leandro Paredes, who was replaced by Ander Herrera, to a thigh injury before Landre was sent off for a dangerous challenge on Rafinha.
Mbappe broke the deadlock on 32 minutes, going around keeper Baptiste Reynet before pushing the ball into the empty goal.
PSG, however, lacked Neymar’s creative touch as he was rested for the trip south after returning from international duty for Brazil.