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.
The next two goals came quickly.
Phoenix answered 68 seconds after Pavelski's goal when Moss fought off Nieto and redirected a shot from David Schlemko past Niemi.
San Jose responded on a power play two minutes after that, tying it when Marleau gathered a pass from Tommy Wingels and beat Smith with a wrist shot from between two defenders.
The Sharks made a big push to start the third period, and Burns scored midway through, one-timing a feed from Pavelski behind the net that went through Phoenix defenseman Derek Morris' legs.
Phoenix again had an answer, scoring with just over 6 minutes left on a power play when Mike Ribeiro sent a pass through traffic to Vrbata, who scored his 11th of the season from the left circle to tie it at 3-all.
Smith made a big save on Burns after a turnover right in front in overtime, but couldn't stop Couture or Marleau in the shootout.
"They're such a good team, those first two lines have really good players," Vrbata said. "We played much tighter defensively and didn't give them much. Obviously, (they scored) three goals, but it's a good team."
NOTES: Friday night was the 10th anniversary of the Coyotes' first game at Jobing.com Arena — a 3-1 loss to Nashville. ... Thornton, the NHL assists leader with 37, has five in his past two games. ... Coyotes captain Shane Doan missed his ninth straight game because of Rocky Mountain Fever. He skated Friday morning, but no timetable has been set for his return. ... Couture has gone seven games without a point, leaving him stuck on 99 goals and 98 assists for his career.