Marc-Edouard Vlasic celebrated his 26th birthday by scoring the game-tying goal with 5 minutes left in the third period. Joe Pavelski also scored for the Sharks, extending his streak to four straight games with a goal.
Antti Niemi made 27 saves as San Jose extended its longest winning streak since opening the season with seven consecutive wins. Niemi stopped Antoine Vermette in overtime and turned aside all three shootout attempts.
Boyd Gordon and Radim Vrbata scored for the Coyotes, who have lost eight of the past nine games to plummet in the Western Conference standings.