In-form Belgium midfielder Hazard netted a penalty in the 12th minute and set up Dimitri Payet for the second on the half-hour as Lille stayed third with 56 points from 30 games.
Montpellier, whose game at Olympique Marseille was postponed to April 11 as the hosts prepare for a Champions League match, have 60 points and lead Paris Saint-Germain on goal difference after Carlo Ancelotti's side lost 2-1 at Nancy on Saturday.
"It's too soon to talk about the title," Lille captain Rio Mavuba told French TV channel Foot + with eight games left.
Coach Rudi Garcia added: "We will see. If those in front of us continue to underperform, maybe we will come back".
Toulouse dropped to fifth on 50 points, behind Olympique Lyon on goal difference after the seven-times French champions salvaged a 1-1 draw at Stade Rennes in Sunday's late game.
Lyon, who have played in the last 12 editions of the Champions League, face an uphill battle to secure a place in Europe's premium club competition with Lille likely to finish third and clinch the play-off spot.
On one of them, Toulouse's Pantxi Sirieix got a straight red card for a rough tackle on Nolan Roux in the 83rd minute.
