Burns took a cross-ice pass from Mikko Koivu and beat Evgeni Nabokov over the left shoulder. Owen Nolan also scored in his return to the Minnesota lineup, and Krys Kolanos added a goal to help the Wild complete a 4-9-1 December that saw them go from first to last in the Northwest Division.
"I think we were in a frustrating situation for a while now and we realize we have to get the boat turned around and we went for it," Nolan said.
Minnesota coach Jacques Lemaire said it was probably the Wild's best game, and was happy it came against one of the NHL's top teams.
"We drove at the net," Lemaire said. "We sent pucks there. We got rebounds. We got good opportunities to score there. We made nice little plays."
Devin Setoguchi and Milan Michalek scored for the Sharks, with Michalek tying it at 2 with 25.2 seconds left in regulation and Nabokov off for an extra attacker.
San Jose, tied with Boston for the NHL lead, lost for just the second time in regulation in 21 games -- and the first time in nine games against Minnesota. It was the Wild's first win in 10 games against a Western Conference opponent.
"I thought they didn't play as well as they played in the past. I thought we had a lot of good chances on them," San Jose center Joe Thornton said. "We didn't capitalize like we normally do."
Minnesota thought it had a 2-1 lead when Kolanos shot from the right circle went into the net with under 6 minutes to play. However, the puck quickly caromed out of the net, referee Stephane Auger waved no goal and play continued.
James Sheppard scored from in front 28 seconds later, but after officials reviewed Kolanos' goal it was determined to be good.
"After we scored, we thought both of them should've counted. I guess that's not the rule," Sheppard said, smiling.
Sharks coach Todd McLellan said he was happy Kolanos' goal counted because it put the extra seconds back on the clock, which ultimately came in handy.
Michalek tied in the final minute, fighting off Burns to score off a rebound.
"It was important that we played hard all the way until the end, but disappointing we didn't get the extra point," defenseman Marc-Edouard Vlasic said.
Minnesota was more energetic than it has been in most games.
Nolan, who missed the previous 18 games because of a leg injury, tipped Burns' shot past Nabokov midway through the opening period. It was the first time in 12 games that Minnesota scored the first goal of a game.
Setoguchi scored on the power play midway through the second period, carrying the puck from behind the net and putting a wrist shot from near the left dot behind Niklas Backstrom, who had been penalized for delay of game.
The Sharks third-leading scorer, Setoguchi missed Monday's game following the death of his grandmother.
"It's great to be able to back and contribute," Setoguchi said. "Coach expected me to be better tonight. I had a couple of extra days off. Coach knew I'd be fresh, but I just needed to make sure I was focused and ready to go."
Struggling Minnesota nearly regained the lead a minute later, but Derek Boogaard shot wide of an open net and Burns hit the post. Off a scramble, Andrew Brunette poked in the puck late in the period, but the officials waved it off, saying the play had been blown dead.
"It's a new, clean slate hopefully, and we've got to keep it going. It's big for our confidence," Burns said. "Hopefully we can realize we are a great team in here. There's a lot of stuff outside that we can't control, but in here we've got to believe that we've got a good team. Believe in each other and keep it going."
The worst Western Conference stretch in Minnesota history was a 12-game drought (0-6-4-2) from March 6 to April 4, 2001. ... D Christian Ehrhoff returned to the San Jose lineup after being a healthy scratch Monday in Dallas. Ehrhoff is a minus-6 in his last six games, and hasn't scored in 17 games. ... Nolan's power-play goal was the first by Minnesota in nine home games against San Jose dating to Feb. 7, 2003. ... Kim Johnsson returned to the Minnesota blue line after missing Monday's game due to a family emergency.
Copyright by STATS LLC and The Associated Press
Arena: Xcel Energy Center Location: Saint Paul, Minnesota
Referees: Stephane Auger, Dan Marouelli Linesmen: Lonnie Cameron, Vaughan Rody
Attendance: 18,568 (102.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Owen Nolan (6)
(Power Play) Assists: Brent Burns, Mikko Koivu
Devin Setoguchi (18)
(Power Play) Assists: Rob Blake, Joe Thornton
Krys Kolanos (2)
(Power Play) Assists: James Sheppard, Brent Burns
Devin Setoguchi (19)
Assists: Marc-Edouard Vlasic, Joe Thornton
Brent Burns (6)
Assists: Mikko Koivu, Pierre-Marc Bouchard