After they had spotted the Oilers a 1-0 lead in the first frame, the Sharks reeled off six unanswered goals to win going away.
Dany Heatley's power play goal tied it with less than 4 minutes remaining in the first, and Couture and Pavelski (two assists) extended San Jose's lead in the middle stanza.
Jordan Eberle got a shorthanded tally for the Oilers' only score.
Nikolai Khabibulin was lit up for six goals on 34 shots faced in the loss.
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