Iran Press/ Europe: Terem Moffi gave Nice the lead with a deflected shot into the bottom corner, but Mbappe leveled with a first-time shot from the edge of the area.
Gaetan Laborde bundled the visitors back into the lead, and Nigeria's Moffi hit a fine strike from 18 yards.
Mbappe's flying volley gave PSG hope, but they could not level.
It was the France captain's seventh goal in four games this season after his return to the team, which followed a disrupted pre-season in which he was frozen out of the squad over a contract dispute.
Friendly, managed by 34-year-old Italian Francesco Farioli, moves above PSG in the table into second behind Monaco.
PSG had a presentation before kick-off for nine-time Ligue 1 title-winning midfielder Marco Verratti, who has just completed a move to Qatari side Al-Arabi.
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