SAN JOSE, Calif. — There's something about the San Jose Sharks that brings out the best in Mike Smith and the Arizona Coyotes.

Smith stopped Joe Pavelski in the third round of the shootout to preserve the Coyotes' 3-2 victory over the Sharks on Saturday night.

The Coyotes became the first team to beat the Sharks three times this season, improving to 3-0-1 against them.

"Mike Smith plays well against them. He's really played well," Coyotes coach Dave Tippett said. "I think that's the biggest key, but it's a rivalry game and they're fun games to be involved in."

Smith made 38 saves, including six during a power play in overtime.

Brendan Perlini and Radim Vrbata scored in the tiebreaker for Arizona, and Logan Couture broke through for San Jose.

Shane Doan and Ryan White scored in regulation for the Coyotes, who snapped a two-game skid.

"The whole thing started with Smitty getting bumped and being down 5-on-3 for 2:06," Doan said. "Getting through that definitely creates a little emotion and got Smitty going."

Brendan Dillon and Couture scored and Martin Jones finished with 26 saves for the Sharks, who had won eight of nine.

"You have to make them pay on the power play and we didn't do that," Sharks coach Peter DeBoer said. "You have to give Smith credit. He always plays well against us."

Following a scoreless first period, in which Arizona killed off the 5-on-3 penalty, Doan put the Coyotes ahead with a power-play goal midway through the second period.

Dillon scored his first goal of the season with 2:45 left in the second to tie it.

Couture punched in a puck on a rebound in front of the net to give the Sharks a 2-1 advantage early in the third period that lasted all of 26 seconds.

The go-ahead goal was set up when Mikkel Boedker blocked a clearing pass.

White scored an unassisted goal shortly after to tie the score again.

"That's a tough one to give up on the next shift," Couture said. "You never want to do that. Kind of kills the momentum for the team and drains the energy out of the building. It's something we don't want to continue."

The game remained tied through regulation thanks in part to some nice goaltending on both sides. One Sharks scoring opportunity late was swiped away in front of the net by Doan.

Doan did give the Sharks a power-play opportunity in overtime after tripping Tomas Hertl with 2:51 remaining.

"Shane took two bad penalties, but fortunately our PK came through," Tippett said. "The 5-on-3 kill in the first, and the one in overtime was huge."

Jones laid himself out to stop a Coyotes' scoring chance with 35 seconds remaining.

"That was a fantastic save. It got us a point," DeBoer said. "But a breakdown like that you can't happen so late."

NOTES: With the Coyotes scoring first, it snapped a nine-game streak in which the Sharks scored first. ... Doan scored his first goal in 17 games. ... White scored his third goal in seven games since returning from injury. ... The Sharks' Patrick Marleau has a six-game points streak. ... Couture has points in seven of his last eight games.

UP NEXT

Coyotes: Host Montreal on Wednesday night.

Sharks: At Buffalo on Tuesday night in the opener of an East Coast trip.