Marcelo Bielsa's side had gone four points clear with a 2-0 win at home to Nantes on Friday, but the champions responded in fine fashion at the Parc des Princes.
PSG totally dominated the first half, though Ibrahimovic's penalty was all they had to show as Nice goalkeeper Mouez Hassen routinely denied their star front line.
The mercurial Swede's goal was his first for the club in almost three months, having seen his season so far interrupted by a nagging heel injury.
Nice had won two of their previous three games on the road in Ligue 1 - including an impressive 1-0 win at Monaco - and they had their chances as the second half wore on and PSG began to sit deeper.
However, a combination of wayward finishing and impressive goalkeeping by Salvatore Sirigu maintained the clean sheet which keeps PSG just a point off Marseille.
Though not a precursor for the first half's flow of play, Sirigu was called into an early save by Alassane Plea, but PSG quickly asserted their dominance - Edinson Cavani firing a 20-yard effort wide before Ibrahimovic clattered the post from similar range.
The Parisians' attacking intensity proved too much 14 minutes in though.
Lucas Moura burst into the box only to be felled by a combination of Romain Genevois and Jordan Amavi, with Ibrahimovic sweeping the resulting penalty away with typical swagger.
Cavani could have doubled the lead 10 minutes before the break, but found Hassen too tough to beat as the angles narrowed for him in the left channel.
The electric pace of Lucas and Serge Aurier down the right flank was causing Nice constant problems, but they clung on to the interval just a goal behind.
Ibrahimovic had been favouring his previously injured ankle late on in the opening half, but came out seemingly fine after the break.
Plea remained Nice's sole attacking threat - hurdling a pair of weak challenges before following up with a weak shot at goal.
Aurier again put the afterburners on to leave left-back Amavi standing, but his whipped cross was tough for Cavani to control and the Uruguayan's header flew over.
Amavi himself then had Nice's best chance, keeping a deep cross from the right in play as the PSG defence dozed and lashing a low shot which Sirigu kept out with his legs before seeing a header from a corner loop wide.
Nice's resurgence was ultimately quelled by the hosts, though, who remain undefeated this term and travel to Lille on Wednesday once again looking to hunt down leaders Marseille.
