In-form Belgium midfielder Hazard opened the scoring from the spot and set up Dimitri Payet for the second on the half hour as hosts Lille stayed third with 56 points from 30 games.
Montpellier, whose game at Marseille was postponed to April 11, have 60 points and lead Paris St Germain on goal difference after Carlo Ancelotti's side were humbled 2-1 at Nancy on Saturday.
Lille, who have now won their last three league games, were in a class of their own in the first half and Toulouse were lucky to reach halftime with only two-goal deficit.
Hazard converted from the spot after he was brought down in the box to give Lille a 12th-minute lead.
Payet then chested the ball down from a Hazard cross and volleyed home to make it 2-0 and it took a couple of fine saves by Ali Ahamada to keep Toulouse in contention.
They reduced the arrears on the hour when Serge Aurier netted from close range as Lille sat back and waited for counter-attacking opportunities.
On one of them, Toulouse's Pantxi Sirieix was shown a straight red card for a rough tackle on Nolan Roux.
"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
Turkey striker Mevlut Erding struck after five minutes for the hosts with a low, angled shot and two minutes later team mate Jonathan Pitroipa outmuscled Dejan Lovren in the box but his attempt smashed against the post.
Lyon were denied a possible penalty early in the second half when substitute Jimmy Briand appeared to have been brought down by goalkeeper Benoit Costil.
However, Lisandro Lopez equalised 14 minutes from time when he connected with a Clement Grenier free kick to beat Costil from close range.
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.
In the third Ligue 1 match of the day,