Adrien Thomasson fired home the only goal after 68 minutes at the Stade de la Beaujoire as Nice were punished for failing to properly clear a cross.
Nice had ridden their luck until that point, with Nantes hitting the woodwork on three occasions -- once through Emiliano Sala's first-half header before US international Alejandro Bedoya struck the post and then the bar in the space of five minutes.
Nice remained two points behind both Lyon and Monaco in fourth place as Nantes snapped a run of five games without a win.
Lyon host 17th-placed Gazelec Ajaccio later on Saturday, while Monaco are at home to Guingamp and Saint-Etienne take on relegation strugglers Toulouse as the battle for Champions League qualification intensifies.
On Friday, Zlatan Ibrahimovic scored twice as Paris Saint-Germain thrashed Rennes 4-0 to equal their own Ligue 1 points record.
Ibrahimovic increased his goals haul to 34 for the season with Maxwell and Edinson Cavani netting either side of the Swede's brace as PSG moved onto 89 points, matching their total from 2013-14, with three games still to play.