"Great players make great plays at the right time, and he's one of those guys," Sharks coach Peter DeBoer said. "He thrives in those moments. He wants to be out there in those moments. That's not an accident that happens to guys like that."
After Joe Thornton won a faceoff in the left circle, Pavelski got the puck, spun and shot from the high slot to beat Wild goaltender Darcy Kuemper.
"It's always a broken play usually when you get it and they're coming out hard," Pavelski said. "The guy had his stick out and [I was] just trying to pull it and get it in. Usually there's a little bit of a screen. It kind of worked out perfect there. I don't think he saw it until the end. It definitely wasn't going to beat him with its speed. Good feeling to see that one go in."
The goal was Pavelski's 23rd of the season.
"I've been here with [Pavelski] for seven years now and he's done the same thing over and over again," Sharks center Logan Couture said. "I'm used to it. I'm sure our fans are used to it. You don't realize how impressive it is when you're going through it. I'm sure one day we'll sit back and look back at everything he's done and kind of realize how impressive it is."
Kuemper, who had a 25-save shutout against the Sharks on Dec. 12 here, made 29 saves for the Wild (23-17-8).
"I looked one way around the traffic and he shot the other way," Kuemper said. "I felt pretty good, which I wouldn't normally say after giving up four goals. I felt like I made a lot of good saves. I thought we did a pretty good job on the penalty kill. You don't want to give those guys too many chances, but three is not many."
Tomas Hertl, Joonas Donskoi and Joel Ward scored for the Sharks (25-18-3), and Martin Jones made 25 saves to win his sixth straight. Pavelski and Joe Thornton each had two assists.
The Sharks won for the seventh time in their past eight games and are in second place in the Pacific Division with 53 points. They're 4-0-1 in their past five home games after starting 5-12-0.
"I look at the standings every day and it's nice to be in a playoff spot," Couture said. "But you can never get comfortable. This race is so tight, you lose a couple in a row and you're out of the playoffs. We've got to continue to pick up points."
Chris Porter, Charlie Coyle and Jarret Stoll scored for Minnesota (23-17-8).
The Wild defeated the Los Angeles Kings 3-0 on Thursday, their only win in their past seven games. They finished a four-game road trip 1-3-0.
"A tight game like that, late in the game, you want to at least get a point," Stoll said. "You have to lock these games down. The last minutes of any period is huge, not just the third. It's very frustrating. We worked hard. I felt our game was coming and we were getting chances. We tie up like that, we have to get a point out of it."
Minnesota led 2-1 in the first period, but Donskoi and Ward scored in a span of 1:38 midway through the second.
Donskoi scored a power-play goal at 12:20, taking a cross-ice pass from Ward and beating Kuemper with a one-timer from the left circle. It was Donskoi's seventh goal of his rookie season.
"I thought he was outstanding tonight, maybe one of the best players on the ice on either team," DeBoer said of Donskoi. "He's moving his feet, he's attacking, he's playing with confidence. I thought he was great."
Ward gave the Sharks a 3-2 lead at 13:58 with his 14th goal. Donskoi missed wide right on a 2-on-1 rush, but the puck bounced off the end boards to Couture below the goal line. Couture passed to Ward, who beat Kuemper from the left circle.
"Got some timely plays, some timely goals, and that's what we need, just to capitalize and find a way somehow to create some momentum, create some chances and try to finish," Ward said.
The Wild tied it 3-3 at 12:10 of the third period when Stoll put the puck under Jones' pads from the slot on a rebound for his third goal. Jonas Brodin's shot from the point bounced off Jones' chest to Stoll.
Pavelski kept the game from going to overtime with his 43rd NHL game-winning goal.
"That is a real tough way to lose a hockey game," Wild coach Mike Yeo said. "It's disappointing because at that point, you think you're good to get a point. You climb back into it, you have to find a way to get the point. Getting into a little bit of penalty trouble in the second changed the momentum of the game. Scoring three goals is great but, obviously, you can't give up four."
The Sharks took a 1-0 lead at 1:33 of the first period on Hertl's ninth goal, third in his past four games. Pavelski shot wide right, and Hertl took the puck behind the net to the other side and banked it off Kuemper before he could recover.
Thornton got the secondary assist to extend his point streak to eight games. He has a point in 16 of his past 17 games. With his two assists, he ranks 16th on the NHL assist list with 930; he caught and passed Larry Murphy.
Porter scored his third goal of the season at 13:00 of the first period to tie it 1-1. He established position in front of San Jose's net and knocked in a rebound after defenseman Marco Scandella's point shot bounced off his skate.
Coyle scored a power-play goal at 19:36 to make it 2-1. Jared Spurgeon's slap shot from the point hit the crossbar, and Nino Niederreiter sent a short pass to Coyle, who beat Jones from close range. Coyle, a former San Jose prospect, scored his 12th goal.
Wild forward Jason Pominville played in his 800th NHL game.
