Laurent Blanc's men were handed a huge boost ahead of the midweek Champions League quarter-final first leg as Thiago Silva played the full 90 minutes despite suffering a fractured cheekbone last week but produced an unconvincing performance at the Allianz Riviera.
Yet the league leaders were still able to claim all three points and move 13 clear of Monaco ahead of their trip to Evian on Saturday.
The left-back looked to have been pushed in the back by Edinson Cavani in the lead up to the goal, which was allowed to stand as PSG claimed their 23rd league win of the campaign.
Blanc's focus will now switch to Wednesday's Chelsea game as PSG look to reach the Champions League semi-finals for the first time since 1995.
Nice did cause the PSG defence the occasional difficulty but it was Blanc's men who continued to create the better chances, Cavani drawing a fine save from David Ospina before Marquinhos headed wide from the resulting corner.
But the Colombia international was finally beaten seven minutes into the second half as Ibrahimovic headed Javier Pastore's cross into the path of the unfortunate Kolodziejczak to bundle home.
Eric Bautheac did come close to equalising for Nice from a free-kick, but Claude Puel's hosts were grateful to former PSG midfielder Mathieu Bodmer for keeping the deficit at one.
