World Cup star Mbappe stole in at the far post in the 67th minute for his 13th league goal of the season, making him France's top scorer with Neymar away on holidays in Brazil.
PSG coach Thomas Tuchel can also go on holiday relaxed with his club on 47 points, as second-placed Lille, 13 points adrift, lost 2-1 at home to Toulouse.
With Neymar away, Argentine Angel Di Maria was in the line-up and came close to making it 2-0, forcing a fine save from Ciprian Tatarusanu, who then watched Di Maria hit the crossbar from the rebound.
Meanwhile, third-placed Lyon drew 1-1 at fourth-placed Montpellier after opening the scoring thanks to their captain Nabil Fekir before a great header from Ruben Aguilar gave the surprise-package southerners a share of the spoils.
Henry's Monaco were dreadful and the former Arsenal striker spat on the ground after Nolan Roux of Guingamp made fools of the Monaco defence to make it 2-0.
Monaco were champions in 2017 but now have 13 points from 18 matches, just two more than Guingamp.
Strasbourg paid hommage to the victims of a terror attack that killed five people on December 11 in their first home game since as they won 2-0 against Nice.
Meanwhile, Marseille, in sixth, drew 1-1 at Brittany outfit Angers and fifth-placed Sant-Etienne beat Dijon 3-0.