Eric Staal and Suter each had a goal and two assists, Zach Parise had two assists, and Dubnyk made 27 saves for Minnesota (1-1-1).
"We needed that one," Parise said. "It was a little bit of a slow start for us and they capitalized on some good chances. [Dubnyk] made some really good saves to keep it 2-0 and I felt like once we started to play a little smarter in the neutral zone and continually get it behind them, we started to get the puck back a little more. That's where our offense started from and we got our legs. We got that rare short-hander at the end to tie it up. It was a good win."
Alex DeBrincat had two goals and an assist, Jonathan Toews had two assists, and Ward made 42 saves for Chicago (2-0-2), which is the second team in NHL history to open the season with four consecutive overtime games (New York Rangers, 1997-98).
"We should've been able to put it away," DeBrincat said. "We should've been able to keep it in their zone and maybe even get a few scoring chances. They're a good team and they played well all game and [Ward] played outstanding for us tonight. It could've been a different score at the end of the game and when we have that chance to win we can't let it slip away."
DeBrincat scored at 10:07 of the first period to give the Blackhawks a 1-0 lead on a one-timer after Toews split Wild defensemen Suter and Matt Dumba and passed to him in the left circle.
Dominik Kahun scored his first NHL goal on a one-timer low in the right circle to make it 2-0 at 12:50. Staal cut it to 2-1 at 13:19 of the second period with a tap-in at the left post after a cross-crease pass from Zucker.
Zucker tied it 2-2 with three seconds left in the second period on a shot from the slot that went under Ward's arm.
DeBrincat scored his second of the game 10 seconds into a power play at 2:29 of the third to make it 3-2. He has seven points (four goals, three assists) in a four-game point streak.
"The game was there for us," Ward said. "It was disappointing to let a point slip away against a divisional opponent, but they worked hard to fight back. There's chances obviously in overtime that could have gone either way. It's unfortunate we let it slip away."