Leivo, who was acquired in a trade with the Toronto Maple Leafs on Monday for Michael Carcone, scored on his first shot to give the Canucks a 1-0 lead at 7:02 of the first period. He took a centering pass from Elias Pettersson off the rush and used Wild defenseman Jared Spurgeon as a screen to beat Dubnyk high blocker side.
"He's got eyes in the back of his head and sometimes when you least expect it, it's on your tape. So I've just got to be ready whenever he's got the puck," Leivo said of playing with Pettersson. "It's exciting. I've got to make the most of it. I thought I battled hard and I've just got (to get) used to the speed. I'm not used to playing against the top line."
Parise redirected a one-timer from Matt Dumba to tie it 1-1 at 12:17.
Motte scored on a rebound in the left circle that went under Dubnyk's pads to make it 2-1 at 9:56 of the second period.
Dubnyk, who had allowed 19 goals in his previous five starts, made 14 saves in the third period, including a glove save on Pettersson on a partial breakaway at 7:52 and against Brock Boeser on a backdoor chance with 12 seconds left.
"It's just been a really weird stretch," Dubnyk said. "Not seeing a lot of shots, pucks finding their way in for whatever reason. You have to try harder and harder each game to not let it affect what you are doing and not to squeeze the stick. Tough way to start tonight when you are trying to get rid of that, but it was nice to get some work and get some shots and get back to the way we are used to feeling in here."