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Defending champions Paris Saint-Germain had put the pressure on Lyon with a 3-1 win over Lorient on Friday that sent the capital club a point clear at the summit.
And Hubert Fournier's men duly wilted as Nice produced a superb away performance to put extra breathing room between themselves and the relegation zone.
Carlos Eduardo opened the scoring for the visitors with a stunning overhead kick in the 23rd minute before Alassane Plea saw a second goal for Nice chalked off by the offside flag.
Lyon midfielder Maxime Gonalons levelled matters from the penalty spot in 56th minute after Lloyd Palun had been shown a second yellow card for bringing down Nabil Fekir.
But Nice refused to lie down and secured all three points four minutes from time through Valentin Eysseric's spot-kick following Bakary Kone's ill-advised challenge on Plea.
