ST. PAUL — Higher-seeded teams with the lead in a best-of-seven series over the history of the NHL playoffs have had plenty of trouble putting the opponent away.

Sometimes the brink of elimination has been what truly gets a team going.

Consider the Chicago Blackhawks, though, when their foe is down. An ability to swoop down and delivering the finishing victory has become a clear trait of this team since coach Joel Quenneville took over and stars Patrick Kane and Jonathan Toews arrived.

“The bigger the setting, the bigger the stage, they seem to rise to that challenge,” Quenneville said.

Since 2009, the first postseason appearance for Kane and Toews, the Blackhawks have not lost in any of the seven playoff series they’ve been in that were tied after four games. That’s a 13-0 record in Games 5 and 6 of such matchups that were even at two each, including the Stanley Cup finals in 2010 against Philadelphia and 2013 against Boston.

They’ll test that perfect mark once more on Tuesday in Game 6 against the Minnesota Wild, who fell behind 3-2 in this Western Conference semifinal series after losing 2-1 in Chicago on Sunday.

“To do exactly whatever it takes … is one of the hardest things in any series, to clinch it,” said Blackhawks left wing Bryan Bickell, who’s tied for the NHL lead with six goals this year in the playoffs.

“But I feel we have the confidence and the poise and the relaxation that we don’t get ahead of ourselves and just play shift by shift.”

During the Kane-Toews era — which includes left wing Patrick Sharp and core defensemen Duncan Keith, Brent Seabrook, Niklas Hjalmarsson — the Blackhawks are 11-2 in games played with a chance to win a series.

They’re 5-1 on the road, with the only losses in those clinching situations against Vancouver, in 2011 in Game 7 of the first round and in 2010 in Game 5 of the second round. They rebounded in 2010 to win Game 6 and advance.

The Wild are bound to be one of the toughest outs these Blackhawks have encountered. They’re 5-0 at Xcel Energy Center since the playoffs began, outscoring their opponents 16-5 and allowing an average of 19.2 shots on goal per game. The Blackhawks were stifled in Games 3 and 4, unable to amount any kind of offensive rhythm.

“The building has been electric. The fans have been unbelievable. I’m sure they’re having a good time with the late starts,” Wild defenseman Ryan Suter said, smiling. “Everything, it’s been a lot of fun for us. We’re driving to the rink and you see the excitement outside the rink, and we just build off that.”

The Wild won two elimination games in the last round against Colorado and, to factor in franchise history, are 9-5 all time in those situations. They’re trying to become the first NHL team to force consecutive Game 7s in the same postseason without holding a series lead since the New York Islanders in 1987.

“Just get ready for Game 6 here. That’s our Game 7 right now,” captain Mikko Koivu said.

Quenneville declared injured center Andrew Shaw out again for Game 6. Wild coach Mike Yeo said left wing Matt Moulson and defenseman Keith Ballard were skating on Monday but declined to speculate on their status.

Suter took a hard spill in Game 3 in a tangle with Blackhawks right wing Marian Hossa, leaving the game briefly with an apparent injury to his right arm, but he and Yeo have said repeatedly he’s fine.

Really, at this point in the playoffs, any pain is mostly an afterthought. So, too, is the elimination scenario for the Wild.

“I think we like the challenge. We always seem to make things harder than it needs to be. I don’t know if that’s a good thing to do, but it seems throughout the year that’s kind of been the way we’ve gone about it,” Suter said.

So the teams will take the ice on Tuesday, with the pressure on each side higher than it’s been all season.

“I think we know what they’re doing. I think they know pretty much what we’re doing, too,” Blackhawks defenseman Johnny Oduya said. “From this point I think it’s just a matter of will and who wants to win the most and who’s fresher and who plays better.”