After Jeremy Menez's first-half opener, Ibrahimovic scored his 27th goal of the Ligue 1 season and fed Clement Chantome for the third to put PSG on 70 points with five games left, nine ahead of second-placed Marseille.
In the process, PSG also dented Nice's hopes of playing in next season's Champions League.
Nice, who finished the game with 10 men after keeper David Ospina was shown a straight red card, slipped down to sixth on 54 points, five behind third-placed Olympique Lyon.
PSG, who are unbeaten in their last 14 home games in all competitions, were looking to make amends for Wednesday's elimination in the French Cup quarter-finals by Evian Thonon Gaillard.
"I still don't understand today how we could be so bad against Evian and so good today," PSG coach Carlo Ancelotti told French TV channel Canal Plus.
"We started well with a lot of intensity and aggressiveness. That was the key. Now what we need to do is be more consistent."
Ancelotti's side got off to a brilliant start, with Javier Pastore and Ibrahimovic tormenting the visitors' defence.
Ibrahimovic chested down a delightful looped pass from Pastore, only for his cross-shot to hit Ospina's right post.
On a swift counter attack, Pastore and Ibrahimovic played a fine one-two before the Argentine midfielder toyed with Ospina in the box and then set up Menez with a cutback for the France international to poke the ball into the empty net.
Menez had a chance to double the tally in the 28th, but shot straight at Ospina from point-blank range after Ibrahimovic had headed the ball into his path.
Ibrahimovic and Nice centre back Renato Civelli tried repeatedly to provoke each other, with the Argentine even kissing his opponent on the neck shortly before the break. Both players were handed a yellow card.
Nice, who were without injured striker Neal Maupay and suspended forward Eric Bautheac, struggled to threaten the PSG defence.
Ospina was sent off in the 63rd minute when, after fluffing a routine clearance, he fouled Ezequiel Lavezzi.
Ibrahimovic converted the resulting penalty before his excellent pass was met by second-half substitute Chantome, who poked the ball home for the third with two minutes remaining.