The Coyotes picked up their 14th road win, second most in the league, despite being outshot 34-15. Bob Essensa had 34 saves in his first shutout this season and 17th of his career.
It was the fifth straight loss for San Jose, the last two coming in overtime.
San Jose went 0-4 on the power play and is 0-19 with the man-advantage in four games.
The Coyotes were outshot 26-8 over the first two periods but fended off the Sharks, killing two successive power plays midway through the second, including a 5-on-3 that lasted for 1:06.
Both sides missed solid opportunities to score.
With just seconds left in the second, Jeremy Roenick skated in on a breakaway and unleashed a slap shot that Shields managed to stop with a glove save 10 feet in front of the net.
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