Brady Tkachuk scored, Jake Sanderson and Claude Giroux each had two assists and Anton Forsberg made 26 saves for the Senators (19-19-3), who had lost two straight after winning four of five.
"You don't want long losing streaks," Ottawa coach D.J. Smith said. "I think this team's capable of having some kind of run, whether it's now or whenever. Every win in this League gives you a bit of confidence, especially on the road."
Video: OTT@ARI: Tkachuk starts scoring in 1st period
Dylan Guenther had a goal and an assist, and Karel Vejmelka made 42 saves for the Coyotes (13-23-5), who are 0-7-0 since winning three in a row.
"We're going through a tough stretch right now, and we've got to crack it," Arizona forward Lawson Crouse said. "It's frustrating going through this right now, no one's happy about it."
Smith moved DeBrincat up to play with Tkachuk and Tim Stutzle after a 3-0 loss to the Nashville Predators on Monday, and the switch paid off immediately.
Tkachuk made it 1-0 at 7:49 of the first period, knocking in a rebound of DeBrincat's shot for his second goal in three games.
"With our team, there's a lot of guys that, after one shift, you get a lot of chemistry from, a lot of chances," Tkachuk said. "I love playing with them, and I feel like we had a lot of great looks tonight."
Coyotes forward Clayton Keller drew a five-minute major penalty and was ejected for cross-checking Senators defenseman Erik Brannstrom at 11:19.
Arizona began with 11 forwards and seven defensemen, so Keller's absence left them with 10 forwards for the rest of the game.
"It's a tough situation to lose a good player early in the game like that," Coyotes coach Andre Tourigny said. "But the way the guys responded to it was really good. … We fought hard. I just wish we had a defended a little better. We didn't find a way to get out of that slump."
Derick Brassard made it 2-0 at 14:45 on the ensuing power play, shoving the puck under Vejmelka's left pad after Giroux steered it towards the net.
Video: OTT@ARI: Brassard doubles Senators' lead in 1st
Tourigny unsuccessfully challenged for goalie interference, drawing a delay of game penalty, but Ottawa couldn't score during a 5-on-3 power play lasting 1:34.
Guenther cut it to 2-1 with a power-play goal at 8:45 of the second period, his first goal in three games since returning to the NHL after helping Canada win the gold medal in the 2023 IIHF World Junior Championship.
"I'm just trying to use that momentum from the World Juniors, play with a little more confidence," Guenther said "You go there, you touch the puck more, play in more situations, and I'm coming back and trying to play like that here."
DeBrincat made it 3-1 at 17:41, jamming in the puck after initially missing off the rebound of Tkachuk's shot.
Video: OTT@ARI: DeBrincat nets 14th goal of season in 2nd
Crouse cut it to 3-2 at 3:45 of the third period, scoring off Nick Bjugstad's backhand pass to the post.
"We probably could have scored three or four early in the third, and they get one chance and it goes in," Smith said. "It tests your mettle a little bit. But to their credit, the guys stayed with it and found a way to win."
Mark Kastelic made it 4-2 at 9:42, beating Jakob Chychrun to the net to redirect Sanderson's shot. Kastelic grew up in Phoenix and played three seasons with the Junior Coyotes youth team.
"I've been looking forward to this trip for a long time, there was the build-up to the game and it all kind of came together, and we got the two points," Kastelic said. "It felt extra special."
Barrett Hayton cut it to 4-3 at 17:16 on a backhand between Forsberg's pads, but Artem Zub scored an empty-net goal at 19:15 for the 5-3 final.
NOTES: Ottawa hadn't won at Arizona since March 9, 2017. … Smith's victory was his 100th in the NHL. … DeBrincat hadn't scored in five games after he had four goals during a three-game streak. … All four of Guenther's NHL goals are on the power play. He has two goals in two games against the Senators. … The Coyotes also had a seven-game skid last season, from April 4-18.
