Lille are third on 71 points, two adrift of leaders Paris St Germain and Montpellier, who can reclaim top spot later on Monday when they face fifth-ranked Stade Rennes.
The northern side are certain to end the season no lower than third as fourth-placed
De Melo scored the opener from the penalty spot in the 26th minute after keeper Alexis Thebaux challenged Eden Hazard on the edge of the box.
The Brazilian striker doubled the lead 10 minutes later when he headed home from a Dimitri Payet corner kick.
Hazard, reportedly the target of several leading European clubs, shone again as he set up Payet for the third goal in the 60th minute.
Auxerre are on 34 points, two from safety while Bordeaux moved up to seventh place on 55 points, two behind Rennes.