SAN JOSE, Calif. -- It took overtime in the third meeting, but the San Jose Sharks finally solved the Arizona Coyotes.

Brent Burns blasted a power-play goal 19 seconds into overtime to give San Jose a 2-1 win, its first in three tries against a last-place opponent that was giving the Sharks fits this season.

"They're a division opponent, and they play hard," Sharks defenseman Brenden Dillon said of Coyotes. "Every game is so close as we've seen for all three now. We understand how important the points are, every hit, every play, every shot, every pass is so important to the outcome."

San Jose, winners of four out of five on its now-concluded homestand, lost by a 3-2 score each of the first two meetings, both in Arizona. The Sharks outshot the Coyotes 41-30 and 45-26 in those frustrating defeats.

And it was a similar contest on Tuesday at SAP Center as the Sharks posted a 42-19 edge in shots on goal.

"They're just tough games," Burns said. "We haven't really found the points from that team this year. I mean, every game is going to be tough. They're no different."

Burns scored the game-winner, his ninth goal of the season, on a feed from captain Joe Pavelski past Arizona goalie Mike Smith. Burns credited Logan Couture, who earned the second assist, for being a key on the play.

"Couch made a great play with the entry, he had good poise with the puck," Burns said.

The Sharks (13-9-1) earned only their second power play of the game with three-tenths of a second left in the third period when Arizona center Martin Hanzal high-sticked San Jose left winger Melker Karlsson.

"It's too bad that power play shouldn't have been at the end, it was a hand pass that wasn't called and they give Hanzal a penalty," Arizona coach Dave Tippett said. "That's the way the breaks go sometimes."

The Coyotes (8-10-3) saw their modest two-game winning streak snapped.

"We've been playing well, but tonight we came up short," Arizona left winger Max Domi said. "We didn't play well enough to win, but we'll take the point."

The Sharks and Coyotes traded goals in the middle period to go into the second intermission tied 1-1.

Arizona broke through at even strength following a San Jose turnover at center. Right winger Radim Vrbata hit a wide-open Domi with a cross-ice pass, and the second-year Coyotes forward went short-side to beat Sharks goalie Martin Jones with a wrist shot from the inside edge of the left circle.

Sharks left winger Patrick Marleau was a full stride behind Domi, who scored his fourth goal of the season at 7:19 on what was the visitors' third shot of the period.

San Jose continued to pressure throughout the middle part of the period, running its shot advantage to 25-10 before finally striking.

Left wing Mikkel Boedker did a nice job to win a battle on the boards and sent a puck deep Chris Tierney, who walked out of the right corner and slipped his second goal of the season between Smith's pads at 15:29.

"We were talking about taking it to the net a couple shifts before that," Tierney said. "When I saw an opening, I decided to take it right there and see what happened. I just kind of got lucky, tried to shove it in, and it ended up in."

The Sharks outshot the Coyotes 14-5 during a scoreless first period that included close calls for each side.

Marleau went top shelf with a backhand shot from the right circle off the rush, but Tippett was successful with a coaching challenge as Dillon was clearly offside -- with both skates, no less -- exactly one minute after the opening faceoff.

The Coyotes had their near miss on the only power play of the period. With Sharks right winger Joel Ward serving a hooking minor, Hanzal redirected a feed from Vrbata behind Jones.

The puck struck the near post, rolled across the goal line and hit the far post, too, before San Jose defenseman Marc-Edouard Vlasic fished it out of harm's way just past the eight-minute mark.

"Anytime you lose, there's frustration," said Smith, who made 40 saves. "I thought we started well. It was one of our better starts in this arena we've had in the first 10 minutes or so. And then it kind of got away from us."

NOTES: Arizona G Mike Smith saw his record against the Sharks fall to 11-8-4. He has four shutouts vs. San Jose. ... LW Melker Karlsson returned to the San Jose lineup after missing seven games with a left ankle injury. ... Arizona played without C Brad Richardson (broken fibula) and G Louis Domingue (lower body) while D Kevin Connauton and D Jakob Chychrun were healthy scratches. ... San Jose RW Tommy Wingels (lower body) didn't skate Tuesday, and he missed his second consecutive game. However, he isn't expected to be out long-term. Sharks C Tomas Hertl (right knee) remains week-to-week. D Dylan DeMelo and LW Matt Nieto were healthy scratches. ... The Sharks visit Los Angeles on Wednesday. ... The Coyotes return to the desert for a two-game homestand starting Thursday against the Kings.