France forward Anthony Martial went off after receiving treatment for an injury during his country's World Cup qualifying win over Kazakhstan.
Martial's clever turn and pass set up Ousmane Dembele to make it 1-0 against the team ranked 122 in the world.
Sergiy Maliy produced a fine clearance as Martial looked to make it 2-0 before the defender headed into his own net.
Manchester United player Martial was replaced by Kylian Mbappe, who had a penalty saved after being fouled.
Having been held 1-1 by Ukraine in Paris last Wednesday, reigning World Cup champions France have four points from two games in Group D.
Didier Deschamps' side are back in qualifying action on Wednesday away to Bosnia-Herzegovina.
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