Mbappe, with a penalty, and Kean found the net in the second half after the visitors had Andreaw Gravillon sent off to move up to second on 31 points from 15 games.
They trail Lille, who beat bottom side Dijon 2-0 away earlier, by one point, and are one ahead of third-placed Olympique Lyonnais after they conceded a last-gasp goal in a 2-2 home draw against 10-man Stade Brestois.
Olympique de Marseille, who have two games in hand, lost 2-1 at Stade Rennais after being reduced to 10 men in the first half.
Lille went ahead in the 19th minute when Yusuf Yazici found the back of the net with a low shot from Zeki Celik's cutback.
They went close to doubling their tally before the break, only for Jonathan Ikone to miss the target with an attempted lob.
Lyon thought a Memphis Depay penalty and Maxwel Cornet's goal in the second half would be enough to beat Brest.
Yet the Brittany side, who had Paul Lasne sent off in the 74th, had opened the scoring though Anthony Lopes's own goal and they snatched a stoppage-time equaliser with a Romain Faivre penalty.
Marseille also finished their game with 10 men after Pape Gueye, who had opened the scoring, was sent off, and Rennes prevailed thanks to goals from Hamari Traore and Adrien Hunou as they snapped the visitors' six-match winning streak.
Elsewhere, fifth-placed Montpellier, who have 26 points, lost 2-0 at home to mid-table Metz and promoted RC Lens moved up two spots to seventh by beating Monaco 3-0 away.