Mbappe converted from the spot in first-half stoppage time after the referee awarded a penalty for handball on a VAR review, restoring PSG's lead following Neymar's early opener and a Duje Caleta-Car equaliser.
PSG are 15 points clear of second-placed Marseille with six games remaining and Mauricio Pochettino's side -- who also have a far superior goal difference -- stand poised to reclaim the trophy they relinquished to Lille last season.
If Marseille fail to beat Nantes on Wednesday then PSG can clinch their eighth Ligue 1 title in 10 seasons if they have a better result against Angers at the same time.
Despite the apparently high stakes for the biggest fixture in French football, there was a distinctly flat atmosphere at the Parc des Princes.