Vegas (45-21-5), which lost a fourth straight home game, leads the Pacific Division by eight points over the second-place San Jose Sharks.
Erik Haula, who was selected from the Wild in the NHL Expansion Draft, scored his fifth goal in six games and had an assist for the Golden Knights.
"We've got to figure it out quick here," Haula said. "We had a good meeting with the guys after the game. We've got to realize we only have a couple handfuls of games left. We've got to start peaking."
Marc-Andre Fleury made 26 saves in his second straight loss after getting his 400th NHL win Monday at the Philadelphia Flyers.
"It's tough to figure out," Fleury said of the home losing streak. "We've had such great success here all year long. Now, it's been a few weeks that we're struggling here. On the road, I think we played the right way, a little more patient, and simple, I'd say. So, I think we need to get back to that."
Zucker scored at 7:19 of the first period to give the Wild a 1-0 lead.
"That was fun. First year ever here for Vegas, and [Zucker's] from here, we wanted to get him one," Wild forward Eric Staal said. "For him to get the first one, to get us on the board, you can't ask for anything better than that."
Coyle scored at 5:53 of the second period to make it 2-0, and Dumba made it 3-0 at 7:36.
"When we win, all season long, we usually outwork the other team," Golden Knights coach Gerard Gallant said. "They came in here and outworked us tonight, that was the bottom line. We still played well, but the urgency wasn't there. I wouldn't say we're playing awful hockey, I'm not going there."
Haula scored at 13:28 of the third period to make it 3-1, and Ryan Carpenter scored with 56 seconds remaining to make it 3-2, before Parise's empty-net goal with 34 seconds left made it 4-2.
