Reims had been unbeaten in nine games, but its task was made harder in the 69th when Wout Faes was sent off for his second yellow card. The home side complained about a preceding foul from Milik in the buildup.
Payet settled the issue with his seventh goal of the season in the 76th.
Milik thought he’d scored a second, too, but that was ruled out for offside, a decision confirmed with a lengthy VAR check.
Reims remained 11th.
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