Laurent Blanc's men went into Saturday's game at the Parc des Princes knowing they could extend their lead at the summit following third-placed Monaco's 1-1 draw with Evian on Friday.
And the champions made no mistake as Ibrahimovic produced a wonderful display to seal the points.
The Sweden international turned home Gregory van der Wiel's volleyed cross to put PSG in front seven minutes prior to half-time, before doubling their lead from the spot 12 minutes into the second half.
Defender Nemanja Pejcinovic pulled one back for Nice on 70 minutes, but their hopes of a fightback were ended when Ibrahimovic capped off his treble with a powerful header from Lucas Moura's right-wing delivery that represents his 50th goal for PSG.
Blanc's side are now four points ahead of Lille in second place following their 0-0 draw at Guingamp.
The hosts were reduced to 10 men when midfielder Lionel Mathis was sent off late on, but Rene Girard's side could not take advantage in a game bereft of clear-cut chances.
Elsewhere, Valenciennes missed the chance to move out of the bottom three as a last-gasp equaliser forced them to settle for a 1-1 draw with Montpellier.
Ariel Jacobs' men took the lead at the Stade du Hainaut after six minutes through Benjamin Angoua's close-range strike, but midfielder Benjamin Stambouli struck in the 91st minute to earn a share of the spoils for Montpellier despite Mathieu Deplagne's dismissal.
Bastia maintained their unbeaten home record as they overcame Rennes 1-0 thanks to an eighth-minute goal from Lille loanee Gianni Bruno.
Bruno held off the attentions of several Rennes defenders to volley past Benoit Costil and secure a win that sees the Corsicans leapfrog Philippe Montanier's side into ninth place.
Meanwhile, Toulouse were held to a 1-1 draw by struggling Ajaccio, as Reims played out a goalless stalemate at Lorient, who had winger Maxime Barthelme sent off in the second half.
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