The home side, beginning the game just two points off the summit, had the first chance of the match when Jonathan Delaplace let rip from outside the box in the sixth minute, but the effort was off target.
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Just a minute later, the visitors countered through Kevin Berigaud, whose long-range shot was blocked, but Lille nearly scored at the other end immediately after, with Michael Frey setting up Marcos Lopes, but the subsequent effort was just wide.
The home side applied constant pressure against their opponents, but despite a multitude of chances, were unable to break the deadlock in the first half.
The second half proved a different affair, as Montpellier came back into the game and applied sustained pressure.
Though Ryan Mendes forced a save out of goalkeeper Geoffrey Jourdren in the 66th minute, Montpellier tightened the screws in the latter stages of the game to guarantee a point as Souleymane Camara and Daniel Congre nearly headed the visitors to victory.
The result keeps Lille in third place, while Montpellier climb to fourth.