Falcao and Mbappe struck before the interval to put Monaco on 80 points from 33 games, ahead of Paris St Germain on goal difference.
French Champions PSG, who beat Montpellier 2-0 on Saturday, have played one extra game.
Nice's slim title chances took a knock when they were held 1-1 at Toulouse, Valentin Eysseric salvaging a point for the visitors when he cancelled out Corentin Jean's opener.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Nice are third on 74 points, with Lyon fifth on 54.
Lyon coach Bruno Genesio, whose side qualified for the Europa League final after a penalty shootout against Besiktas in the week, fielded a second-string team who struggled in the early stages.
Monaco, who have reached the Champions League final four, went ahead in the 36th minute when Falcao headed home from six metres in a packed area.
Mbappe struck, too, just before halftime with a low shot after being set up by Bernardo Silva's through pass. Lucas Tousart pulled one back in the 51st with a header from Memphis Depay's corner.
Earlier, the game between St Etienne and Stade Rennais was interrupted after local fans managed to get into the stadium where the match was being played behind closed doors. Referee Ruddy Buquet sent the players to the dressing-room in the 16th minute.
The fans left the stadium quietly after some 15 minutes and the players came back on to the pitch.
The game, which ended 1-1, was being played behind closed doors after St Etienne were sanctioned for crowd trouble during a derby against arch rivals Lyon in February.
(Editing by Clare Fallon)
