Striker David found the back of the net on 16 minutes to put Lille, who have won their last three games, on 45 points from 21 matches, behind PSG on goal difference.
The result left Rennes on 36 points from 21 games.
Third-placed Olympique Lyonnais are two points behind PSG and Lille after they demolished arch-rivals St Etienne 5-0 away.
At the Roazhon Park, Lille started well as David scored from close range after goalkeeper Romain Salin had tipped a corner into the Canadian's path.
The visitors had a penalty ruled out by the VAR as David was offside when he was fouled by Rennes defender Nayef Aguerd in the 24th minute.
Rennes took no risks for fear of Lille's counter attacks and Christophe Galtier's side comfortably held off the hosts in the second half.
At Geoffroy Guichard, St Etienne were missing 10 players who tested positive for COVID-19 and Les Verts were no match for Lyon.
Kadewere rubbed salt in St Etienne's wounds with a left-footed effort in the 68th minute, after being set up again by Depay, for his ninth goal of the season.
Things got even worse for St Etienne when Denis Bouanga deflected Depay's free kick into his own net with eight minutes left.