Ottawa goaltender Mike Condon was pulled after Stepan's clearing attempt from the Arizona blue line went between his pads for a shorthanded goal to make it 3-0 at 15:30.
Antti Raanta made 25 saves for the Coyotes (6-5-0), who have outscored their opponents 20-4 during their winning streak and 27-10 in their past six games (5-1-0) after being shut out three times in losing four of their first five.
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"I didn't feel panic in the guys, the goaltenders were playing great, we just weren't scoring (early in the season)," coach Rick Tocchet said. "Guys stuck with it and practiced hard, and the goals started to come. We've got a good mojo going now, and we don't want to wreck it."
Alex Formenton scored his first NHL goal for the Senators (4-5-2), who have lost four games in a row. Condon made eight saves, and Craig Anderson made 22 in relief.
"Tough start by us, and we couldn't find a way to claw back in the game," forward Chris Tierney said. "We've got to come for a full 60 (minutes). We've played in spurts for 10 minutes, but you're not going to win in the League if you don't play for a full 60."
Stepan's shorthanded goal was the fifth in three games for the Coyotes, who lead the NHL with six. They're the only NHL team with more shorthanded goals than power-play goals-against (three).