PSG, unbeaten in all competitions in their last 33 outings, have 31 points from 13 games with second-placed Lille on 27 after they secured an eighth consecutive clean sheet in a 0-0 draw at En Avant Guingamp.
Monaco are third after drawing 1-1 at home to Evian Thonon Gaillard on Friday.
Ibrahimovic and Cavani each had a goal ruled out for offside in the opening half hour as PSG piled on the pressure.
But the tall Sweden striker broke the deadlock six minutes before the break after a move involving 25 passes move when he converted Gregory van der Wiel's half-volleyed cross.
He made it 2-0 12 minutes into the second half with a penalty after Cavani, who is himself involved in a World Cup playoff against Jordan next week, was brought down by keeper Luca Veronese.
Nice's Nemanja Pejcinovic tapped home from Gregoire Puel's cross to reduce the arrears 20 minutes from time but any hopes of a point quickly vanished as Ibrahimovic headed in from a cross by second-half substitute Lucas six minutes later.
(Reporting by Julien Pretot; Editing by Tony Goodson)
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