Yakupov's shot got past Roberto Luongo in the first round, and Edmonton's Viktor Fasth was perfect in the shootout.
Matt Hendricks and Jordan Eberle scored in regulation for Edmonton. Fasth made 35 saves for his third win this season.
The Oilers won for the first time in four games and snapped a franchise record 14-game, road-losing streak. The Oilers, who have three road wins this season, earned their first since Nov. 9 at the New York Rangers.
Jonathan Huberdeau and Erik Gudbranson scored for Florida, and Luongo stopped 32 shots. He has lost three straight starts for the first time since the opening three games of the season.
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