A late penalty from defender Cedric Mongongu proved to be the difference between the two sides as Monaco slipped to a defeat that leaves them 13 points adrift of leaders Paris Saint-Germain.
The Democratic Republic of Congo centre-back converted from the spot after Ricardo Carvalho was adjudged to have handled in the area to secure a win that moves them five points clear of 18th placed Valenciennes, who drew 0-0 at Montpellier.
Sochaux are now eight points adrift of safety after Marseille defender Nicolas N'Koulou struck in the 90th minute to earn a 1-1 draw at the Stade Auguste Bonal.
Centre-back Stopilla Sunzu had given Sochaux the lead with his fourth goal of the campaign, only for N'Koulou to net a rare strike and spare Marseille's blushes.
Toulouse came from behind to earn a 2-2 draw against bottom club Ajaccio, who are now 15 points behind Evian with seven games to go.
Goals from Ricardo Faty and Junior Tallo had put the beleaguered Corsicans in command, but midfielders Issiaga Sylla and Clement Chantome found the net to rescue a point for Alain Casanova's men and push Ajaccio closer to the drop.
Reims are without a win in four, but did come from behind to claim a 1-1 draw with Lorient.
Vincent Aboubakar opened the scoring from the penalty spot in first-half stoppage time, but Reims winger Odair Fortes ensured a share of the spoils with a goal four minutes into the second half.
In the other game to be played on Saturday, Nantes played out a goalless draw with Bordeaux.
