Juuso Valimaki and Lawson Crouse scored, and Karel Vejmelka made 22 saves for the Coyotes (3-6-1) after Connor Ingram allowed three goals on 10 shots.
"We were coming off a huge win (3-1 against the Florida Panthers on Tuesday) and emotions were high," Crouse said. "I don't know if they were running too high. They scored on the second shift and then it's boom, boom, boom, boom and it's 4-0. And it's hard to come back in this league when it's 4-0 in the first."
Denis Gurianov scored from the slot 1:27 into the first period to make it 1-0. It was the ninth time in 11 games the Stars have scored the opening goal this season.
"The first shot of the night goes in and obviously it gets the boys going," Wedgewood said. "We had a quick shot, [think] quick mentality, and an early lead is obviously huge. We started great and throughout the whole game we kept them in their end."
Wyatt Johnston made it 2-0 at 3:54 with an unnassisted goal after intercepting Dysin Mayo's breakout pass. Johnston is the first rookie in Stars/Minnesota North Stars history to score at least one goal in three consecutive road games.
"It's really important when you get the first couple of goals, especially in the first few shifts," Gurianov said. "It's like, let's get the boys rolling. Guys feels good when you score the first couple."