The result left PSG in the driving seat with 29 points from 11 games, though second-placed champions AS Monaco can reduce the gap when they visit Girondins Bordeaux on Saturday.
Nice, who finished third last season, stayed 14th with 10 points after their fourth successive league defeat.
PSG were unfazed by the absence of their suspended Brazil forward Neymar, who was sent off in Sunday’s 2-2 draw at Olympique Marseille, as Angel Di Maria made the most of a rare start in the wake of strong competition up front.
The Argentine winger set up both of Cavani’s goals, having whipped in a third-minute free kick from the left which the Uruguay hitman superbly headed home at the near post.
The pair combined again in the 31st as Di Maria carved open the visiting defence with a perfectly weighed pass and Cavani tucked the ball into an empty net after beating the offside trap and rounding goalkeeper Walter Benitez.
Benitez made two good saves in the first half, keeping out easy chances for Cavani and Di Maria to prevent Nice from falling further behind in a lop-sided contest.
He was powerless, however, when centre back Dante put the ball into his own net after Cavani headed a teasing cross from the left back into the six-yard box.
Kylian Mbappe then hit the outside of the post after a dazzling solo run as PSG kept their foot on the gas, with Nice hardly able to get into the opposition half.
Cavani was given a standing ovation by the home fans when he was substituted for Lucas Moura in the 85th minute and Neymar also applauded his team mate from the VIP box.