Duhaime tied it 1-1 at 12:33 of the second period with a high-slot deflection of Brock Faber's shot from inside the right point.
The Wild outshot the Rangers 15-3 in the second.
"We didn't like the second period," Wheeler said. "Obviously, Minnesota is a really good team, they have a lot of pride, so they probably didn't like their first period. But it's not up to the standard that we've set in here and that was the communication after the second, that we're a whole lot better than that.
“We wanted to go out and right off the bat in that third period get back to playing in their zone. 'Bread' (Panarin) and 'Laf' made a great play for a huge goal for us."
Lafreniere put New York ahead 2-1 at 1:41 of the third period by completing a 2-on-1 with Panarin. Panarin's patience forced Wild defenseman Jonas Brodin to defend him in the right circle, leaving Lafreniere open on the left side. Fleury was stuck at the right post and didn't get over in time to stop Lafreniere.
The rush started when Faber pinched down from the point into the right circle but missed the puck. Trocheck pushed it up to Panarin in the neutral zone and the Rangers had the 2-on-1.
"It was just stupid, plain and simple," Faber said of his pinch. "I looked at it on the bench and kind of hoped I saw something different, but I didn't. It was a complete lack of judgment that cost us."
Wheeler pushed it to 3-1 at 14:39 with a power-play goal, scoring off a rebound of Will Cuylle's shot after Lafreniere's initial shot from the right point.
Wheeler signed a one-year contract on July 1.
"It was a good moment to score a goal to extend the lead late in the third period," Wheeler said. "It was a perfect way to get one."
Panarin scored an empty-net goal at 18:39 for the 4-1 final.