Christophe Galtier's men move again above Marseille, who received at Bordeaux on Friday, on goal difference.
But they're nevertheless 10 factors adrift of runaway leaders Paris Saint-Germain who visit Lyon afterward Sunday.
Kasper Dolberg gave the visitors a thirteenth-minute lead, but Morgan Schneiderlin was shown a instantly red card for a address on Christophe Herelle just seven mins later.
Brest then dominated the in shape, playing 62 percent ownership and having 26 attempts at goal, with Nice goalkeeper Walter Benitez pressured into 10 saves.
But Nice struck again with 11 minutes closing, as Amine Gouiri teed up Andy Delort to attain. Gouiri added further gloss to the scoreline in stoppage time along with his 9th league purpose of the season.
