Dimitar Berbatov scored a 57th-minute winner as Monaco extended their Ligue 1 unbeaten run to six matches with a 1-0 win at Lille.
The Bulgarian headed home Yannick Carrasco's free-kick and could have added a second late on when he flashed a volley just wide.
Joao Moutinho also missed two good chances in what was a dominant display from the visitors.
For the hosts it was a second consecutive defeat after their recent good form had moved them away from the relegation zone.
Montpellier are now six...