The Coyotes gave up an early score and trailed throughout the game until Nick Johnson produced a power-play goal with just 19 seconds left in regulation.
That earned Phoenix a point after Yakupov managed his fourth goal of the season. Taylor Hall put a shot on goal in the overtime, but it bounded off the glove of defenseman Ray Whitney. Yakupov was there to bat the puck past goaltender Chad Johnson.
Lennart Petrell scored on a wrist shot for Edmonton just 4:51 into the game.
The victory went to Devan Dubnyk, who made 27 saves and narrowly missed recording a shutout. It was Edmonton's third win in four games.