Rene Girard's men remain in the UEFA Champions League spots in third, but are now just one point above fourth-placed Saint-Etienne and are 13 adrift of league leaders Paris Saint-Germain.
Mathieu Bodmer's strike in first-half injury time was enough to complete victory at the Allianz Riviera, moving the hosts up to ninth.
Lille have now gone five matches without a victory in France's top flight, and will be keen for a swift response at home to Sochaux next Saturday.
Marseille and Lyon both failed to take full advantage in their quest to reach third, with the former drawing 2-2 at home to Toulouse, while the latter fell to a 2-0 defeat at Rennes.
Dimitri Payet and Mathieu Valbuena scored either side of Wissam Ben Yedder's leveller, as Marseille led 2-1 at half-time at the Stade Velodrome.
But Etienne Didot equalised on the hour mark as Alain Casanova's side left with a share of the spoils.
Lyon's three-match winning run in Ligue 1 ended at the Stade de la Route de Lorient.
Cedric Hountondji had fired the hosts into a 22-minute lead, while Samuel Umtiti's straight red card four minutes before the break further hindered Lyon.
Transfer-window signing Ola Toivonen notched his maiden goal for Rennes to complete the win after 66 minutes.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
