GLENDALE, Ariz. -- Petr Prucha crashed the crease and got the game-winner.
"It was a great play by Doaner," Prucha said. "He passed me to the open net and I had the easy job."
"Penalties put you behind the eight ball," Stars coach Dave Tippett said. "Those are the things you do to shoot yourself in the foot and we have enough holes in our feet already."
Brendan Morrison, Hutchinson, Darryl Sydor, Chris Conner and Loui Eriksson scored for the Stars, who have lost seven straight. Dallas is 4-12-2 since moving a season-best eight games over .500 on Feb. 19.
Upshall gave Phoenix a 5-3 lead with 8:02 remaining on a wrist shot from the top of the left circle.
But Conner took a long outlet pass from Morrison behind the Phoenix defense and scored on the breakaway with 5:26 remaining and Sydor scored from the right wing with 57.4 seconds left to send the game into overtime.
"I thought we played a really solid hockey game for about 55 minutes," Coyotes coach Wayne Gretzky said.
Morrison gave Dallas a 1-0 lead at 2:04 of the first on a wrist shot over Bryzgalov's right shoulder. Upshall tied the game with a power-play goal nearly six minutes later, taking a pass from Matthew Lombardi on the right doorstep and flipping a wrist shot into the net.
Lisin, who had been a healthy scratch in nine straight games, snapped a 1-1 tie with 7:44 left in the first period when he pulled the puck to his forehand only to watch it bounce off a defenseman's stick and past Stephan from the front of the crease.
"It was very nice getting back in the lineup," Lisin said. "It [being scratched] is part of the job. It's not the first time. You just have to a professional, practice hard and wait for your chance."
Hutchinson tied the game 2-2 at 1:16 of the second period when his one-timer bounced through traffic in front of the net and past Phoenix goalie Ilya Bryzgalov.
Doan scored 31 seconds later on a knuckling one-timer from the left faceoff circle and Lisin added his second goal at 4:32 of the period on a wrist shot into to the top right corner to give the Coyotes a 4-2 lead.
"They got up early on us and I thought it was crucial that we just stuck to the game pland and kept things simple," Upshall said.
Eriksson cut the lead to 4-3 on a power-play goal with 4:49 left in the second.
"There's just a little thing missing from my game right now," said Stephan, who made 27 saves. "I'm always right there but if just a little quicker or in better position and I make the save. I think I'm really close but not quite there."
- Lisin had played in only two of the Coyotes last 13 games.
- Emergency callups Dan Jancevski and Garrett Stafford both played for the Stars in place of defensemen Stephane Robidas and Mark Fistric. Robidas is day-to-day with a lower-body injury and Fistric is day-to-day with an upper-body injury.
- RW Krystofer Barch, D Trevor Daley and C Brian Sutherby also are day-to-day with lower-body injuries for Dallas.
- The Coyotes are 4-0-1 in their last five games against the Stars.
- Bryzgalov had a 127-minute shutout streak against the Stars snapped on Morrison's goal.