Hamhuis fired in a wrist shot at 2:13 of the extra period off assists from Henrik and Daniel Sedin to chalk up the first two-goal game of his career and extend the Canucks' winning streak to three games.
Erick Belanger, Shane Doan and Lauri Korpikoski scored for the Coyotes, who have lost six of seven. Korpikoski's goal at 19:17 of the third period tied the game 3-3 and sent it into overtime.
Ilya Bryzgalov turned back 35-of-39 shots in the loss.
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