Marleau also scored as the two longtime Sharks shined one day after signing three-year deals that will keep them in San Jose through the 2016-17 season.
"For me and Patty both to score, it's a great night for us," Thornton said.
"They're our guys, and we need them when we're down," Irwin said. "Jumbo got us to within one and Patty tied it up and obviously Jumbo won it in overtime. They're our guys. It's just kind of ironic what happened."
Darcy Kuemper made 29 saves as Minnesota lost for just the fourth time in 12 games this month.
"We got a point against a good team in a tough building to play," Ballard said. "For the most part we played a fairly solid game. We weren't the best at times. But we hung in there and even after they got those two quick goals, I thought we responded pretty well. We just couldn't find the time to get the third one tonight."
Thornton and Pavelski combined on the game-winning play by causing a turnover at the blue line. Pavelski then fed Thornton, who beat Kuemper with a wrist shot from the top of the circle to end it with his ninth career overtime goal and first since Nov. 26, 2008, against Chicago.
Pavelski assisted on both of Thornton's goals in a bit of a role reversal after Thornton helped set up many of his 19 goals in the previous 21 games.
"I've been telling Pav, `You've been scoring too much. Start passing the puck.' And he finally listened," Thornton said. "I don't too often, but Pav just made two good plays and luckily I put them in."
The Wild struck first on a nifty play by Cooke midway through the first period. Cooke deflected Thornton's cross-ice pass to Brad Stuart in the neutral zone. Cooke then beat Stuart to the loose puck and skated in on Niemi before beating him with a forehand for his eighth goal.
They added onto the lead early in the second when Mikael Granlund fed Ballard for a one-timer that beat Niemi. It was Ballard's first goal since Oct. 6, 2011, for Vancouver against Pittsburgh, ending a drought of 114 games without a goal.
But that was all the Wild would get as they managed just 12 shots in the final 39-plus minutes. They spent much of the game on the defensive as they won just 18 of 59 faceoffs.
"We lost the extra point because of the face-off circle tonight," coach Mike Yeo said. "We spent the entire night chasing and it's inevitable that they will put you on your heels and give them some momentum. We never started with the puck. That was the big story."
Minnesota dominated the opening half of the second period, limiting San Jose to one shot in the first 11-plus minutes before Thornton and Marleau delivered a day after getting their new contracts.
Thornton struck first when Pavelski fed him for a one-timer that he knocked past Kuemper on a knuckler.
Just 49 seconds later, Marleau scored his 22nd of the season when Tommy Wingels fanned on the original shot but still managed to get the puck to Marleau, who deflected it past Kuemper to tie the game.
Thornton has 40 career multigoal games. ... Minnesota F Jason Pominville got his 500th career point with an assist on Ballard's goal. ... San Jose juggled its top two lines the second half of the game with Matt Nieto playing with Thornton and Pavelski and Brent Burns moving to a wing with Marleau and Wingels.