Mbappe's second-half penalty, when Andrew Gravillon was sent off, and Moise Kean's strike helped PSG to victory after Lille, who host the Champions League runners-up on Sunday, beat Dijon by the same scoreline.
Lyon dropped to third place, a point behind PSG, after a dramatic 2-2 draw with Brest.
Marseille, who have two games in hand on the top three, slipped five points behind the leaders after a 2-1 defeat at Rennes.
PSG coach Thomas Tuchel after the game said that Neymar, who sprained his ankle last Sunday against Lyon, could return this weekend.
"For Neymar we will do everything -- that is the good news," said the German. "I can't say 'No, he's not playing against Lille'. It is possible. We can try, we will try everything."
PSG had 81 percent of possession in the first half against struggling Lorient without creating many clear-cut chances, with Lorient's Teremas Moffi wasting the best opportunity of the opening period when he fired wide when clean through on goal.
But the match was effectively decided less than five minutes after the break, as visiting full-back Gravillon was harshly sent off for a nudge on Mbappe in the box.
The forward, sporting a striking new blue hairstyle, stepped up to power the spot-kick into the bottom corner.
It took Tuchel's men 10 more minutes to secure victory, with Rafinha setting up Kean to grab his eighth goal since joining PSG on loan from Everton in the close season.
Lyon were a goal down at half-time against Brest after goalkeeper Anthony Lopes's own goal, but Memphis Depay's penalty and a goal for Maxwel Cornet looked to have seen them keep pace with Lille.
But Romain Faivre scored a re-taken spot-kick in the 93rd minute after Brendan Chardonnet's initial effort was saved by Lopes, who was off his line.
Marseille led at Rennes through Pape Gueye, but the midfielder was sent off in the 36th minute and goals from Hamari Traore and Adrien Hunou ended the home team's nine-match winless streak.
Elsewhere, fifth-placed Montpellier slipped six points behind Lille with a 2-0 home defeat by Metz, while Monaco fell to a third straight league loss, beaten 3-0 at home by Lens.