Ben Smith scored the game-winner at 15:30 in overtime for the Stanley Cup champion Blackhawks, who forced a decider on Tuesday in Vancouver and are now seeking to become just the fourth team to rally from a 3-0 series deficit in the playoffs.
The winner of the series will meet the Nashville Predators, who advanced to the second round of the playoffs for the first time after their 4-2 victory over the Anaheim Ducks.
Nick Spaling scored two goals for the Predators, who also clinched the best-of-seven series 4-2.
The Philadelphia Flyers were also on the verge of elimination but instead forced a Game Seven with their 5-4 overtime triumph over the Buffalo Sabres.
Ville Leino scored the game-winner at 4:43 in overtime, after Scott Hartnell had forced the extra session at 10:43 in the third.
Game Seven is on Tuesday in Philadelphia.
Chicago’s charge to their series deciding game was set up by Michael Frolik’s game-tying score at 2:31 in the third before Smith clinched it with his third goal of the post-season.
“Never in a million years did I think it would happen,” Smith told reporters. “I was able to get the rebound and put it over (goaltender Roberto Luongo). It’s pretty amazing.
“Guys kept battling and stuck with it and we’re going to Vancouver.”
Defenseman Brent Seabrook sparked Chicago with his return to the lineup after missing the last two games when he suffered a blow to the head.
Daniel Sedin, Alexandre Burrows and Kevin Bieksa all scored for the Canucks who traded goals with the Blackhawks through regulation.
Nashville had previously reached the post-season five times and lost in the first round each time before Sunday’s breakthrough.
Teemu Selanne and Jason Blake scored for Anaheim who tied the game 2-2 in the second before Spaling gave Nashville a 3-2 lead early in the third period.
David Legwand then converted an empty-net goal with 10 seconds left to clinch the victory for the Predators.
In Buffalo, Philadelphia defenseman Chris Pronger returned to the lineup following a 21-game absence due to a broken hand, but he could do little to stop the early surge from the home team.
Thomas Vanek scored twice in the first period as Buffalo built a 3-1 lead and chased Philadelphia goaltender Michael Leighton who was replaced by Brian Boucher.
Flyers winger James van Riemsdyk scored in the second where Danny Briere added his second goal of the game to tie it at 3-3 before Nathan Gerbe put Buffalo back ahead with a wrist shot at 16:09 in the second.
