They forced at least one more with a furious finish.
Parise scored early and late on tipped shots, and the Wild tacked on two empty-net goals for a 5-2 victory over the Colorado Avalanche on Monday night that sent the first-round playoff series to a decisive Game 7.
"It's one of those nights where you just want to keep touching it and keep having the puck," said Parise, who added two assists for a career-playoff-high four points.
The teams will meet in Denver on Wednesday night, with the winner taking on the defending Stanley Cup champion Chicago Blackhawks in the Western Conference semifinals.
"We don't have any time to hang our heads here and feel sorry for ourselves," Avalanche captain Gabriel Landeskog said. "We're just going to get right back on the horse here and get ready for Game 7."
Ah, Game 7. An already-tight series will produce one final dramatic performance.
"We didn't sign here to win a first-round game. We look at the big picture," said Parise, who joined close friend Ryan Suter in signing 13-year, $98 million contracts with the Wild two seasons ago.
The Wild were in trouble at the second intermission after what Avalanche coach Patrick Roy said might have been his team's best period of the whole series.
Parise scored just 49 seconds into the game on a power play and Mikael Granlund made it 2-0 later in the first period, but a costly turnover by Suter at the end of a failed 5-on-3 situation led to a short-handed goal for the Avalanche when Paul Stastny scored for the fourth time in the series.
Nick Holden got the tying goal in the second period to stop the power-play skid for the Avalanche, who had been denied by a resurgent Wild penalty-kill unit in 19 of 20 previous opportunities in the series. The Wild stumbled through to the second intermission, lacking the edge they had here throughout Games 3 and 4 and in the first period of this Game 6, and the atmosphere in the building became anxious, with one more goal by the Avalanche holding the power to end the home team's season.
So Wild coach Mike Yeo gave his team a spark by reuniting Parise on the first line with center Mikko Koivu, who had two assists.
"I think we started to get a little bit of fear in our game. Not necessarily afraid of them, just afraid maybe of what we were losing," Yeo said, adding: "Both of those guys were leading the charge up front and for me, their determination, their kind of get-after-it attitude, I wanted those guys going out together."
Parked in the crease with the season on the line, Parise took a shove in the back from goalie Semyon Varlamov and then outmuscled defenseman Erik Johnson for position on Koivu's shot from behind the circle that he knocked in with his stick with 6:29 left in the game.
Roy pulled Varlamov with 2:44 remaining, and this time the daring move backfired after it led to tying goals for the Avalanche in Games 1 and 5. Jason Pominville and Marco Scandella found the back of the net for the Wild, and the celebration was on.
Matt Duchene returned to the Avalanche lineup and notched an assist in extensive time on the power play, after missing the last month due to a left knee injury. The Avalanche leader with 70 points during the regular season, Duchene wasn't cleared for action until minutes before faceoff.
"He was flying out there. He was playing well. He was playing hard," Roy said.
He wasn't the only one. Ryan O'Reilly had two assists, and the Avalanche refused to express any frustration afterward, even though they'll be in an elimination situation for the first time in the series.
"If that's what it's going to need to be, then that's what it's going to need to be," Avalanche right wing P.A. Parenteau said. "It's been a battle back and forth with the Wild. We're lucky we have the home ice advantage, but we're going to have to be ready."
The Wild went 18-4-2 when Parise scored a goal in the regular season. ... Duchene said he felt alright: "You've got to learn to trust an injury like that coming back, and as the game wore on I felt a lot more confident with it. There's still a long ways to go."