Nick Foligno and Jason Dickinson each had a goal and an assist, Tyler Johnson had three assists, and Connor Bedard had two assists for the Blackhawks (16-42-5), who had lost six straight and 14 of 15 (1-11-3).
Chicago hadn’t won on the road since a 5-3 victory against the Tampa Bay Lightning on Nov. 9 (0-21-1).
“It feels good, for sure,” Bedard said. “It’s one win, and [in a] long season it's not huge, but especially with the streak we've been on, it's really nice to get a couple of points and obviously have some positivity. It’s the first happy plane ride we've had in a little bit.”
Arvid Soderblom made 37 saves for his first win since Nov. 24 (0-12-1).
“He played so great,” Bedard said. “There’s been so many games where he's kept us in it and we weren’t able to pull it out for him. Tonight he was our best player, and it’s a plus to see him get a win.”
Nick Bjugstad and Michael Carcone scored for the Coyotes (25-32-5), who have lost five straight at home and 15 of their past 17 games overall (2-13-2). Connor Ingram made 27 saves.
Chicago was 4-for-5 on the power play after scoring four power-play goals in its previous nine games.
“I'm guilty, we're all guilty in this room of taking penalties, and it's just a tough one when you’re in the box and [give up a goal],” Bjugstad said. "We didn’t put up much of a fight as far as pushback, and it's not an acceptable effort.”