"I think we're feeding off each other," Perry said about his power-play unit. "We know where each other's going to be. [Gurianov] has a great shot from that side, [Hintz] is controlling the puck on the other end, and you have Miro [Heiskanen] up top."
Jamie Benn appeared to score for Dallas at 13:38, but Tocchet challenged the play for offside, and the call was reversed after a video review.
The Coyotes outshot the Stars 21-13 in the first period.
"I thought we had a good pushback in the second half of the first period and had 21 shots in that first period," Hill said. "We have to find a way to win the game."
After Benn was assessed a boarding major and game misconduct for his hit on Coyotes defenseman Oliver Ekman-Larsson, Taylor Hall scored on the ensuing power play from the top of the right circle through a screen to tie it 1-1 at 12:32 of the second period.