PSG, who host Basel in their Group A third game on Wednesday, got off to a brilliant start before letting Nancy back into the contest.
The French champions moved up to second with 19 points from nine matches, four behind leaders Nice who beat Olympique Lyonnais 2-0 on Friday.
They lead third-placed Monaco, who slumped to a 3-1 defeat at Toulouse on Friday, on goal difference.
PSG went ahead in the 13th minute when forward Lucas scored with a long-range free kick.
It took the visitors five minutes to double the tally. Uruguay striker Cavani intercepted Michael Chretien's poor header towards Ndy Assembe and easily beat the keeper.
Unai Emery's side, who are still far from the level they displayed under Laurent Blanc last season, then let Nancy control the game and paid for it in the 55th minute.
Former France international Alou Diarra, who joined from Charlton during the close season, scored on his first appearance with a header into the top corner from Benoit Pedretti's free kick.
Nancy continued to push but in vain and they stay bottom of the standings on five points, having scored only four goals this season.
On Sunday, troubled Olympique Marseille, who have nine points and lie 14th, host promoted Metz.
(Reporting by Julien Pretot; Editing by Clare Fallon)
