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.
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.
Read the full article on eurosport.co.uk: Monaco back on top of Ligue 1 after win against Lyon