Mbappe struck in the 74th minute to put PSG on 80 points from 29 games and on the brink of retaining the title with second-placed Lille, who beat Nantes 3-2 away earlier on Sunday, still 20 points behind having played a game more.
Thomas Tuchel's side will be crowned next weekend if they beat Racing Strasbourg and Lille fail to win at Stade de Reims.
PSG are looking to become the first club in the French top flight to reach 100 points and to beat the record of most goals scored (118), held by RC Paris since the 1959-60 season.
PSG were without Neymar, who is still nursing a foot injury, Argentine winger Angel Di Maria and Uruguay striker Edinson Cavani, leaving the scoring responsibilities to Mbappe.
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The world champion duly delivered.
PSG dominated but Eric Choupo-Moting skied a sitter over the bar and Marquinhos had a goal disallowed for offside after a VAR review.
Mbappe, however, found the back of the net with a neat strike from inside the area from a Thilo Kehrer cross 16 minutes from time.
Lille claimed an impressive comeback win at Nantes.
The Canaries were 2-0 up after a penalty by Valentin Eysseric and a second-half strike from Kalifa Coulibaly.
The visitors, however, turned the situation around in eight minutes.
Rafael Leao volleyed home to reduce the arrears in the 62nd minute and Nicolas Pepe levelled with a penalty in the 68th before Jonathan Bamba gave the northerners all three points a minute later by poking the ball home from Pepe's cross.
Lille lead third-placed Olympique Lyonnais, who beat Stade Rennais 1-0 away on Friday, by four points.
(Reporting by Julien Pretot; Editing by Ken Ferris and Pritha Sarkar)
