Timothee Kolodziejczak scored an own goal after the break to hand PSG, who are on 76 points with seven games left, their seventh league win in a row.
Second-placed Monaco travel to Evian Thonon Gaillard on Saturday.
Laurent Blanc's side, who host Premier League leaders Chelsea in the first leg of their Champions League quarter-final tie on Wednesday, were in control throughout at the Allianz Riviera but they failed to impress.
Blanc rested four of his usual starters as he left centre back Alex, fullback Maxwell, as well as midfielders Blaise Matuidi and Marco Verratti on the bench.
The attacking trio of Ezequiel Lavezzi, Edinson Cavani and Zlatan Ibrahimovic, however, all started.
Argentine forward Lavezzi missed a couple of chances in a dull first half during which Thiago Silva came close with a downward header and Nice had a Mathieu Bodmer goal ruled out for offside.
Eight minutes into the second half, Kolodziejczak deflected a cross from Ibrahimovic into his own net.
Nice had their best chance one minute from time when Salvatore Sirigu punched away Christian Bruls's 25-metre strike.
- Sports & Recreation
- Laurent Blanc
- Evian Thonon Gaillard
- Zlatan Ibrahimovic
- Ezequiel Lavezzi