Connauton gave the Coyotes a 1-0 lead at 4:06 of the first period when his shot from the top of the right face-off circle beat goalie Kari Lehtonen high to the glove side through a Christian Fischer screen. It was Connauton's first goal in 40 games, dating to Oct. 10 at the Vegas Golden Knights.
"We knew they were going to come out strong, and they did and we didn't answer, so that's a box unchecked," Shore said. "Credit the leaders in this room. There was still 40 minutes left to play, down one."
Shore tied the game 1-1 three minutes into the second. Jason Spezza and Coyotes defenseman Niklas Hjalmarsson slapped sticks behind the net, causing the puck to go over the top of the net to Shore, who batted it out of the air on his backhand.
Seguin scored on the power play at 5:21 to give Dallas a 2-1 lead.
The Stars thought Jamie Benn gave them a 3-1 lead at 10:30 of the second, but Tocchet challenged that Benn was offside, and the goal was overturned after video review.
Janmark made it 3-1 at 13:24 when he scored from the goal line to the left of Wedgewood.
Lindell scored into an empty net with 1:36 left to make it 4-1.
The Coyotes were 0-for-6 on the power play.
"We practiced three days of power play and I thought we had good power-play practices," Tocchet said. "Obviously, tonight, some guys didn't look good out there."