PSG came to life when Lucas released the run of Pastore and the forward maintained his composure to fire a low effort into the bottom corner and hand his side the lead.
The home side rallied on the stroke of half time when Benrahama tried a speculative effort from distance, which hit Mathieu Bodmer in the box. The visitors appealed for offside, but the striker was played on by Luiz and was able to beat Salvatore Sirigu to level the scores.
In the second half, PSG nearly retook the lead when a clearance looped kindly to Luiz on the edge of the box, and the Brazilian fired an effort on the volley that was well saved by Simon Pouplin.
The home side threatened at the other end and only a smart save from Sirigu kept Eduardo's header out of the net, as the Italian tipped his effort past the post after the forward had beaten Luiz in the air.
Luiz continued his eventful afternoon as he was denied a goal by the woodwork after meeting a cross from the right with a bullet header.
However, PSG did retake the lead through Pastore, who juggled the ball past three Nice defenders in the penalty area before powering a volley at goal. Pouplin made the save to deny the midfielder, but he was the first to react to the rebound.
The visitors put the game beyond the reach of Nice when Edinson Cavani was brought down in the area by Jordan Amavi and a penalty was awarded. The striker took the spot kick himself and made no mistake to find the bottom corner.
Valentin Eysseric nearly capitalised on a mistake from Adrien Rabiot as he raided forward to curl an effort towards the top corner, but he was denied by Sirigu as Laurent Blanc's men held out for the victory.