After a goalless first half, Mbappe converted an Angel di Maria cross from the right with an audacious backheel.
Neymar sealed the points five minutes from time when he converted from the penalty spot after on-loan Inter Milan striker Mauro Icardi was fouled.
It was Neymar’s fifth goal of the season and his first since 5 October.
The forward thought he had given the champions the lead in the first half before VAR ruled the strike out.
Thomas Tuchel’s side, who have a game in hand on second-placed Marseille, travel to Montpellier on Saturday (16:30 GMT).