The Sharks won their third in a row and improved their road record this season to 8-1-3.
This was only the seventh NHL appearance in three seasons for Stalock, who made 30 saves.
The lone goal for the Oilers was scored on the power play by Nail Yakupov late in the middle period.
Edmonton lost its fifth in a row. The Oilers have won just four times in 21 games.
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