Younes Belhanda, Remy Cabella and Olivier Giroud (pictured) were on target between the 53rd and 67th minutes as Montpellier chalked up 49 points from 23 games.
Olympique Lyon, who host APOEL Nicosia in a last-16 Champions League game on Tuesday, slumped to a surprise 2-1 home defeat against Caen that left them in fourth place, 10 points off the pace.
Romain Hamouma opened the scoring for the visitors after 13 minutes with a low, angled shot following a quick counter-attack.
Caen made it 2-0 thanks to a superb goal by substitute Livio Nabab who volleyed into the top corner from outside the box 17 minutes from time.
Lyon pulled one back when Lisandro Lopez converted a penalty after Alexandre Lacazette was brought down in the 86th minute.
"We were caught cold," home striker Bafetimbi Gomis told French television.
"Trailing when it's cold like that is not easy. We need to work hard to improve if we want to keep pace with the top teams."
Montpellier needed 53 minutes to warm up, breaking the deadlock through Belhanda's penalty after Henri Bedimo was fouled in the box.
Giroud then set up Cabella for the second and Ligue 1 top scorer Giroud netted his 16th goal of the season after outstripping the defence.
A Mevlut Erding goal was all Stade Rennes needed to see off bottom club Sochaux 1-0 and move up to fifth on 39 points.
Sixth-placed Olympique Marseille's trip to Evian Thonon Gaillard was postponed on Saturday due to a frozen pitch.
‘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
