Laurent Blanc's side recorded a seventh straight win to move 13 points clear of Monaco at the top of the table thanks to a gift from Nice's versatile full-back.
The hosts held their own for the opening 45 minutes at the Allianz Riviera, but could have fallen behind had any of Marquinhos, Javier Pastore and Ezequiel Lavezzi shown more composure from close range.
Nice, who were unbeaten in three games prior to kickoff, posed a threat themselves although mostly from distance, with Didier Digard, Mathieu Bodmer and Valentin Eysseric all testing Salvatore Sirigu.
It only took nine minutes of the second half for PSG to sneak ahead, as Ibrahimovic's cross towards strike partner Edinson Cavani was flicked into his own net by the unfortunate Kolodziejczak.
Eric Bautheac came close to scoring an equaliser for Nice when his 67th-minute free kick went narrowly over the crossbar, and the same player forced Sirigu to save well at his near post on 89 minutes.
PSG hung on to claim victory, but will have to improve with sterner tests on the horizon, most notably the first leg of their Champions League quarter-final with Chelsea at Parc des Princes on Wednesday.