Emmanuel Riviere was on hand to grab the only goal of the game 10 minutes after the restart, finishing calmly from close range following some great work from Jeremy Toulalan.
The result leaves Claudio Ranieri's side 10 points adrift of leaders Paris Saint-Germain in second place, although the former Chelsea boss will probably be resigned to the fact that a dramatic title win is looking unlikely.
Monaco overturning PSG's lead is arguably almost as unlikely as Ajaccio preserving their Ligue 1 status - the bottom-of-the-table side will be relegated if Guingamp avoid defeat at Nantes on Sunday, despite picking up a 1-1 draw at home to Bordeaux.
Their relegation looked to have been sealed when Jussie struck midway through the second half to give Bordeaux the lead, only for Mehdi Mostefa to level with a stunning late volley.
Despite such an encouraging performance, the Corsicans remain 15 points from safety, meaning they are all but down already.
Things look a little better for struggling Sochaux, who kept their survival hopes alive with a 2-0 victory over Toulouse, courtesy of goals from Jordan Ayew and Roy Contout.
Elsewhere, Lille tightened their grip on third place after Divock Origi's second-half strike helped them overcome Valenciennes 1-0 at the Stade Pierre Mauroy, taking them eight points clear of nearest rivals Saint-Etienne, who play on Sunday.
There was more joy for Evian as they continued their revival by coming from behind to beat Bastia 2-1 at the Parc des Sports, extending their unbeaten run to four games.
In the day's only other game, a late strike from Vincent Aboubakar secured a dramatic 2-1 win for Lorient win away to Nice.
