PSG were without injured forward Neymar and that told in a poor first half as the visitors failed to register an attempt on target until the 47th minute when Ander Herrera swept home.
Nantes were unfortunate not to be a goal ahead at that point, Moses Simon somehow missing an open goal from all of three yards at the Stade de la Beaujoire.
Mbappe added a second from a penalty he won and Pablo Sarabia profited from a defensive error late on to seal the win, but only after Keylor Navas had kept out Kader Bamba's penalty at a delicate point in the game.