Tyler Motte and Shane Pinto each had a goal and an assist, and Mark Kastelic and Josh Norris also scored for the Senators, who have won three in a row at home after starting with two road losses. Drake Batherson, Jake Sanderson and Tim Stutzle each had two assists and Anton Forsberg stopped 20 shots.
Dylan Guenther and Clayton Keller scored for the Coyotes, who have lost four of five this season. Karel Vejmelka finished with 26 saves.
Kastelic and Motte scored 47 seconds apart in the third period to push the Senators' lead to 5-2. Kastelic had a couple of whacks at the side of the goal before knocking the puck past Vejmelka at 6:15. On the next shift,
''It was pretty special to play against them for the first time,'' said Kastelic, a native of Phoenix. ''I skate with a lot of those guys in the summer, and it was just kind of a full-circle moment for me and my parents as well. They came in from Arizona and it's really exciting that we got the win, but we have to put it behind us now and look forward.''
The line of Kastelic, Austin Watson and Parker Kelly had coach DJ Smith talking after the game.
''That's a line for us that plays north-south and gets us playing emotionally the right way. I think they did a heck of the job in the third,'' Smith said. ''The do it right, they go 100 miles an hour and they don't give any time and space. They're good at what they do.''
Batherson took a shot that Vejmelka thought he had trapped, but the puck fell into the crease where Motte was able to push it into the empty net.
Tkachuk scored on a breakaway with 7:52 left to close the scoring.
''I thought we played solid in the first period,'' Arizona coach Andre Tourigny said. ''We had a lot of pressure and urgency. We didn't score but I don't think the period was that bad. We played a really good second period obviously and I think in the third they got opportunistic and that was the game.''
The Senators opened the scoring five minutes into the game when Pinto took a shot from the slot that beat Vejmelka. Norris doubled the advantage as he tipped a point shot past Vejmelka less than two minutes later at 6:17.
The second period started feverishly with three goals in a 2:07 span.
Guenther scored on the power play with a chip shot from the bottom of the circle that beat Forsberg at 1:40 to get the Coyotes within a goal. It was the first NHL goal for the 19-year old Guenther, in his fourth career game.
''They were super stoked,'' Guenther said of his teammates' reaction to his goal. ''I think it's pretty cool when they're just as excited as you are. And it's nice for me, too, to get one here. I've been getting a lot of chances.''
Tkachuk's power-play goal at 3:25 restored Ottawa's two-goal lead as he redirected a perfect pass from Batherson at the corner of the net for a 3-1 lead.
Just 22 seconds later though, Keller banked the puck from behind the net off two Senators players and in to pull Arizona to 3-2.
''I thought we played pretty sloppy in the second period. First period we had some jam, then we took some bad penalties and got out of rhythm on the 4-on-4s, turned some pucks over and didn't do, to me, what we had been doing,'' Smith said.
Coyotes: At Columbus on Tuesday night to conclude a season-opening six-game trip.
Senators: Host Dallas on Monday night in the fourth of a five-game homestand.
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