More than two hours later, Vermette scored the clincher in the fifth round of the shootout, securing a 3-2 victory at SAP Center and avenging a 4-1 loss to San Jose in the second game of the season.
"It's nice, especially in this building, to take the crowd out of it," Vermette said of his early goal. "If you can take the lead early on, it's ideal. We'll take that. That was a big goal for us. But with that being said, they never gave up. I think they generated a lot of momentum from their power play, and we found a way to win. So we'll take that."
The Coyotes won their fourth straight game and handed the Sharks their first home loss of the season after five straight regulation wins. San Jose has lost two straight games for the first time this season.
Phoenix coach Dave Tippett became the franchise's all-time leader in victories with his 166th win, snapping a tie with Bob Francis.
Logan Couture scored for the Sharks in the first round of the shootout, and Radim Vrbata answered with a goal in the second round for Phoenix. Vermette ended the game, beating Sharks goaltender Antti Niemi with a backhand shot, moments after Mike Smith rejected Patrick Marleau's shot.
"I tried to come in one angle, change my angle, change my speed to make the goalie adjust a little bit," Vermette said. "I made a move and slid it between his legs."
"It's a huge win against an upper echelon team in the League," Smith said. "I think we can gain some confidence from a game like that. We weren't really thrilled with the way we played, but I think we grounded it out Coyote ugly and found a way to get the two points, and that's all that matters."
Mikkel Boedker also scored for the Coyotes in regulation.
Defenseman Dan Boyle, returning to the lineup after missing seven games with a concussion, and Pavelski scored for the Sharks. Niemi made 28 saves, and Couture had a career-high 10 shots.
The Sharks outshot the Coyotes 16-7 in the first period and15-7 in the second -- 17 of those 31 shots came during five power plays -- but the score was tied 2-2 entering the final period.
San Jose kept firing shots, and Smith kept rejecting them. With six minutes left to play, Joe Thornton got the puck in the slot and ripped a shot, but Smith snagged it.
Then with 33.1 seconds left in regulation, Couture jammed the puck past Smith from close range, but it stopped an inch in front of the goal line. The Sharks still had time for two more shots before the third period ended.
"We had every opportunity to finish it, to end it," Sharks coach Todd McLellan said. "We had some good looks. I'm not sure how hungry we were around the blue paint or how much we were in the goaltender's eyes. He looked comfortable in there, and when a guy like that gets comfortable he makes a lot of saves."
Smith stopped 47 of 50 shots during the Coyotes' loss to San Jose on Oct. 15, but he dug himself an early hole that night. This time, he was sharp from the outset.
"I felt pretty good," Smith said. "After the first period I was a little nervous that my legs and my wind were hemmed in there for most of it, but as the game went on I felt I got stronger and stronger and felt a lot more comfortable. That's good to see."
The Sharks had 50 shots to 23 for Phoenix at the end of regulation, but the Coyotes turned up the heat and outshot San Jose 7-0 in overtime. Niemi rejected every puck that came his way, sending the game to a shootout.
The Coyotes had been outscored 17-5 in the first period of their first 14 games, but they took a quick lead on Vermette's goal.
The Sharks had trouble trying to clear the puck out of their end, and Phoenix made them pay.
Boyle sent a weak pass toward Brad Stuart along the boards, and Stuart tripped over Boedker then fell to the ice.
Rob Klinkhammer got the puck and zipped a pass to Vermette, who snapped a shot from the left circle off a post and past Niemi.
"It was good work on the forecheck," Vermette said. "We kind of turned the puck over."
The Sharks went 0-for-3 on the power play in the first period and wasted a great opportunity when Vrbata went to the box for four minutes after high-sticking Sharks defenseman Scott Hannan in the face and drawing blood at 14:39. The Sharks had eight shots during those four minutes with a man advantage, but Smith stopped every one.
The Sharks got untracked in the second period, scoring two quick goals to take a 2-1 lead. Pavelski scored from the right circle on a 2-on-1 rush at 1:16 of the second, faking a pass to Matthew Nieto and knocking the puck past Smith, just inside the right post.
Then at 5:10 of the period, Boyle scored a power play goal with Kyle Chipchura in the penalty box for slashing Demers. After scoring, an emotional Boyle pumped his fist, then punched the glass. It was his second goal of the season and came in his first game since being knocked out on Oct. 15 against the St. Louis Blues, when Maxim Lapierre hit Boyle from behind and sent him face-first into the boards.
"That definitely felt good, as you could tell by my reaction," Boyle said. "I guess I just made a good shot.
"I expect a lot out of myself, and at the same time I had to be realistic and understand I wasn't going to be as good as I wanted to be. I didn't feel like my normal self, but I will get better in a hurry. I just felt a half-second behind everything."
Pavelski had the primary assist on Boyle's goal, and Thornton had his 800th career assist.
The Coyotes didn't have a shot on goal until 8:57 of the second, but Boedker made it count. He took a long pass from Derek Morris along the right boards, got a step on Marc-Edouard Vlasic and scored from a sharp angle.
Sharks defenseman Matt Irwin was a healthy scratch. It was the first time he wasn’t in the lineup this season.
Coyotes center Mike Ribeiro played in his 800th NHL game.