Nice had won four of its matches but it was Monaco which took the lead in the 29th minute when Cesc Fabregas found Golovin, whose shot went inside the near post. Monaco thought it had doubled its lead two minutes later through Islam Slimani but it was ruled out on video review as Gelson Martins had been offside in the buildup.
Patrick Burner leveled for Nice early in the second half but Golovine netted again in the 74th, after more good play from Fabregas. The Russia midfielder then turned provider with an assist for Wissam Ben Yedder to score Monaco's third goal six minutes later.
Dijon remained the only club without a win in the French top flight as it drew 0-0 against Marseille.
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