PSG headed into Saturday's game at the Parc des Princes knowing they could take command of the the title race after Monaco were held to a 1-1 draw by Evian on Friday.
And the reigning champions took full advantage as Ibrahimovic inspired them to victory, the striker taking his goal tally for the season to 16 in all competitions.
The former Barcelona and Milan star opened the scoring with a close-range strike in the closing stages of the first half, before doubling the lead from the penalty spot in the early stages of the second.
Nemanja Pejcinovic pulled one back for Nice to raise the nerves among the home fans, but Ibrahimovic then eased any tension with a towering header 15 minutes from time.
PSG coach Laurent Blanc handed captain Thiago Silva his first start since picking up a thigh injury in the 1-1 draw with Monaco back in September, while Edinson Cavani was also recalled to the champions’ side after the missing the UEFA Champions League clash against Anderlecht in midweek.
Lucas Veronese replaced the injured David Ospina in the Nice goal as the Cote d'Azur club searched for their first win at the Parc des Princes in four years.
PSG began the game with intent, but it was Nice who could have taken the lead after just three minutes as Thiago Silva's last-ditch challenge denied Dario Cvitanich the chance to convert Christian Bruls’ right-wing cross.
But the visitors were fortunate not to fall behind when Veronese was called into action to keep out Maxwell's far-post delivery shortly after.
The hosts thought they had taken the lead after 25 minutes, Cavani turning home another Maxwell cross, but the goal was ruled out as Ibrahimovic was adjudged to have interfered with play from an offside position.
PSG were undeterred, though, with Ibrahimovic then drawing a fine save from Veronese after latching on a superb throughball from Thiago Motta.
And the capital club were finally rewarded for their persistence seven minutes before the break when Ibrahimovic prodded home Gregory van der Wiel's volleyed cross.
PSG should have doubled their advantage on the stroke of half-time, but Sweden international Ibrahimovic could only nod Motta’s free-kick wide.
Blanc's men continued to dominate after the interval, with Cavani and Ibrahimovic both heading over from close range in the early stages of the second half.
Nice struggled to get a foothoold in the game, and three minutes before the hour mark they fell further behind as Ibrahimovic converted from the spot after Veronese had felled Cavani.
Claude Puel's men did find a way back into the contest with 20 minutes to play, as Pejcinovic tapped in Bruls' low delivery to give the visitors some hope.
But any thought of a surprise comeback was extinguished just five minutes later when Ibrahimovic rose highest to meet substitute Lucas Moura's delivery and complete his treble.
Moura went close himself in the dying stages, but a two-goal lead proved to be more than enough for Blanc's men to take victory.
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