Once San Jose hit the shootout, Logan Couture and Marleau scored, and Antti Niemi stopped Radim Vrbata and Oliver Ekman-Larsson for the Sharks' second win in their past seven road games.
"It's been tough for us on the road, so for us to go out and get the two points was nice," Marleau said.
The Coyotes were much better in their own end than previously against the Sharks, allowing 28 shots in regulation after giving up 101 combined in a pair of games in San Jose earlier this season.
Phoenix pulled out a victory in one of those first two games, but couldn't earn the extra point Friday after struggling in the shootout.
David Moss had two goals, and Vrbata scored late in the third period to help Phoenix earn a point in its fourth straight game — all after regulation.
"The last time we got two points on San Jose, we probably didn't deserve those two points," Coyotes coach Dave Tippett said. "Tonight, I thought that game was a toss-up. Unfortunately, we didn't get the extra point, but we put the work in to get the two points."
With their early travel, the Sharks seemed a step slow in the opening period, and the Coyotes jumped on them, generating several good scoring chances.
San Jose gave them an extra one midway through the period, when Sharks forward Matt Nieto flipped an errant pass right to Moss, who whirled around in the slot and beat Niemi.
The Sharks nearly scored early in the second period when a shot by Justin Braun hit the left post, bounced off a stick and hit the right post before being cleared away.
They did get one through after a Coyotes turnover. Thornton ended up with the stray puck, skated up the middle and found Pavelski, who beat Smith over the glove shoulder from the left circle.