Kane scored two goals in the third period, including a terrific dash through the Minnesota zone for the tiebreaking score, and the Blackhawks beat the Wild 5-2 in Game 1 of the Western Conference semifinals.
Bryan Bickell also scored twice for the Blackhawks, who have won five in a row after losing their first two playoff games. Marian Hossa had a goal and two assists in the first game for the defending Stanley Cup champions since they closed out St. Louis on Sunday.
"We weren't as sharp as we'd like to be," Hossa said. "But as the game went on we improved. But I still think we can play better than we did. Huge win for us."
Game 2 of the best-of-seven series is Sunday.
The Wild showed no sign of any fatigue just two days after their dramatic 5-4 overtime win in Game 7 of their first-round series against Colorado. Playing in the second round of the postseason for the first time since 2003, Minnesota used third-period goals from Clayton Stoner and Kyle Brodziak to tie it at 2.
"We had some good moments in this game, but what it came down to we weren't complete enough in this hockey game," Wild coach Mike Yeo said. "We weren't complete enough collectively and individually."
Brodziak's third goal of the playoffs on a slick pass from Erik Haula silenced the sellout crowd of 21,116 with 13:04 left, but Kane then electrified the United Center once again with his 33rd playoff goal.
The flashy wing carried the puck into the Minnesota zone, hesitated as teammate Patrick Sharp skated behind him, and then split Brodziak and Brodin on his way to the net. He finished the play by roofing a backhand over goaltender Ilya Bryzgalov's left shoulder at 8:22.
"He's so calm with the puck in tight spaces and he makes shots that not a whole lot of people can make," Sharp said. "That backhand is a good example of it. The thing I like about Kaner the best is the big stages, he always seems to put one in."
Kane then celebrated by yelling "Showtime!" twice and pumping his right arm as the delirious crowd cheered wildly.
"Did it look like I said that? Sometimes I don't even know what I'm saying," said Kane, who won the Conn Smythe Trophy for playoff MVP last season. "I was pretty pumped up after that one. You kinda get in your own little world. I don't even know what I said, to be honest with you."
Kane added his fifth goal of the playoffs on a nice pass from Ben Smith, and Bickell had an empty-netter as Chicago pulled away.
"Kane just made a great play," Wild forward Jason Pominville said. "We generated a lot of opportunities. That's the frustrating part. We could have put them away and we weren't able to do it."
Minnesota went 0-for-3 on the power play in a disturbing sign after it struggled with the man advantage in its first-round playoff series against Chicago a year ago. The Wild were unsuccessful on all 17 power-play chances when they were eliminated by the Blackhawks in five games in 2013.
"For the most part, I liked the way we played," Wild star Zach Parise said. "We had some good jump. We had a lot of good zone time. A lot of rush chances. We couldn't capitalize when we needed to and they scored on their power play and we didn't. That was the difference, the special teams."
Bryzgalov had 17 saves in his first start since he was pulled from Minnesota's 4-2 loss to the Avalanche in Game 2. Darcy Kuemper took over for the Wild in net until he got hurt in the third period of the final game, and Bryzgalov made one save to help the Wild advance.
Kuemper is day-to-day with an upper-body injury, but Yeo said before Game 1 against the Blackhawks that the goalie was not in Chicago, making it unlikely that he'll be able to play Sunday.
Bryzgalov got off to a slow start, and Chicago used a pair of high-sticking penalties on Brodin to build a 2-0 lead. Bickell tipped in Brent Seabrook's slap shot at 14:48 of the first, and Brandon Saad had a terrific pass to Hossa for the Blackhawks' second goal in the second period.
Corey Crawford had 30 saves after he made 35 stops in Chicago's 5-1 victory over St. Louis in Game 6, closing out the series for the Blackhawks.
The Blackhawks lost C Andrew Shaw to a lower-body injury in the first period. Coach Joel Quenneville said he is day-to-day. ... Blackhawks F Kris Versteeg was scratched for the second straight playoff game in favor of Joakim Nordstrom. It was Nordstrom's second career playoff game. ... The Wild outshot the Blackhawks 32-22.