Mbappe pounced on a pass from Nordi Mukiele to beat Kasper Schmeichel with a low strike in the 83rd minute of Saturday's match. The France striker tied Neymar as the joint top scorer in the league with eight.
Lionel Messi gave PSG the lead in the 29th with a curling free kick into the top corner from 22 yards. Messi's fifth league goal was one shy of his league tally last season when he took time to adapt to a new club and struggled with knocks and a bout of COVID-19.
Gaetan Laborde equalised from close range just after halftime after the PSG defence failed to clear a cross from Youcef Atal.
Messi shone with Argentina during the international break by scoring twice against Honduras and twice against Jamaica, and could have added a second goal on the stroke of halftime with a powerful strike that Schmeichel tipped over the bar.
PSG needed Messi's brilliance because forward Hugo Ekitike, who got his first start this season, proved toothless and didn't make runs in behind the defence like Mbappe does.
Nice pressed high up the pitch to prevent PSG from creating chances. That defensive ploy worked until the 27th when Messi started a dribbling run, outpacing Mario Lemina before taking on Dante, who tripped the Argentina playmaker and conceded the free kick that led to the opening goal.
Ahead of a key Champions League match at Benfica next week, PSG rested Mbappe and Nuno Mendes until both came off the bench in the second half.
Rennes are starting to gel after an uneven start to the season, climbing to fifth place after beating 10-man Strasbourg 3-1.
Strasbourg defender Gerzino Nyamsi was sent off for planting his studs into Benjamin Bourigeaud's thigh with his follow through after clearing the ball in the 28th. That was not long after veteran striker Kevin Gameiro had a goal disallowed for offside.
Arnaud Kalimuendo took advantage in the 38th by controlling a cross from Adrien Truffert to fire into the bottom corner on the turn. Rennes doubled the lead with a low strike from Martin Terrier in the 49th. Kalimuendo set up Amine Gouiri for the third goal in the 61st.
Strasbourg managed a consolation goal from a penalty by Habib Diallo in the 72nd after Rennes right back Hamari Traore brought down Gameiro. They remained in the relegation zone and the only winless team in the league.
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