Carey Price made 26 saves for the shutout and the host Montreal Canadiens beat the Boston Bruins, 4-0, on Monday night to force Game 7.
Thomas Vanek scored twice and Lars Eller and Max Pacioretty also scored for Montreal, which overwhelmed the Bruins to tie the series at three games apiece.
Game 7 is Wednesday night in Boston.
Eller opened the scoring just 2 minutes, 11 seconds into the game after the Bruins misplayed the puck and Eller was alone in front of the net to beat a sprawled-out Tuukka Rask.
Pacioretty made it 2-0 after scoring on a long stretch pass through Rask's legs in the second period.
Before the period was over, Vanek scored on the power play. Vanek added his second of the game into an empty net late in the third.
Rask finished with 24 saves for the Bruins.
The Blackhawks have the Wild right where they want them - which leads the defending Stanley Cup champions to believe they're about to face the fight of their season.
With a 3-2 series advantage, the Hawks can advance to the Western Conference finals with a victory Tuesday night at the Xcel Energy Center.
Rangers goalie Henrik Lundqvist was fined $5,000 for emptying his water bottle onto Sidney Crosby while the Pittsburgh Penguins captain was involved in a scrum in front of the New York net during Game 6 at Madison Square Garden.