PSG made light of their numerical disadvantage when Siaka Tiene guided home Guillaume Hoarau's cross for the opening goal five minutes after the restart.
Defender Steven Paulle levelled for the hosts off Gael Kakuta's 76th-minute corner.
But the undermanned visitors were not to be denied.
A 90th-minute counterattack saw Jeremy Menez play in substitute Kevin Gameiro, and the striker duly dispatched a shot past Dijon goalkeeper Baptiste Reynet to seal all three points for PSG.
Montpellier dispatched Caen 3-0.
Karim Ait Fana put Montpellier ahead five minutes into the second half at the Stade de la Mosson.
They had to wait until the 82nd minute for Souleymane Camara to double the lead, with Olivier Giroud's 91st-minute penalty adding gloss to the scoreline.
In the other match on Sunday, Yacine Brahimi's equaliser helped Stade Rennes salvage a 1-1 draw at home to second-bottom Auxerre, who had led through Dennis Oliech's early strike.
