The France international, who joined Marseille in January 2017, latched onto Clinton N'Jie's incisive pass before effortlessly skipping by Oukidja and slotting home the hosts' second goal in their 2-0 win at the Stade Velodrome on Tuesday night.
Oukidja was unable to see the match out, having pulled up with a serious-looking knee injury.
The 29-year-old had to be substituted for back-up goalkeeper Kossi Agassa, who played out the last minute of the contest.
Payet has three goals and as many assists from 15 Ligue 1 starts this season for Marseille, who move up to second with their third straight league win.
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