De Melo scored three minutes into added time as Lille, on 31 points from 17 games, stayed one point ahead of Paris Saint-Germain who triumphed 2-1 at Valenciennes thanks to a Nene double.
Elsewhere, Lorient thrashed struggling RC Lens 3-0 and Nancy eased away from the relegation zone by beating Sochaux 1-0.
Champions Olympique Marseille, third on 27 points, lost ground when they drew 1-1 at Auxerre after playing 52 minutes with 10 men following the dismissal of Stephane Mbia.
Mbia was shown a straight red card after bringing down Julien Quercia in the box, Valter Birsa converting the resulting penalty.
Marseille had opened the scoring in the eighth minute through Loic Remy's header from a Brandao cross.
At Avignon, Lille were boosted when the hosts had Jamel Ait Ben Idir sent off for a second bookable offence in the 53rd minute.
Lille piled on the pressure and were rewarded when De Melo headed in a cross from fellow substitute Ludovic Obraniak just seconds before the final whistle.
"It's important to win even when you don't play at your best," De Melo told the Foot Plus TV channel. "It was an important goal, I'm proud I scored it."
PSG are hot on Lille's heels after Nene earned them all three points at Valenciennes with a curling 25-metre shot six minutes from time.
