"It was probably the big play of the game. First, you try to think what their move is as he's coming down the ice," LaBarbera said. "When he came down to the top of the circle, I realized he was going to go low-blocker and I was able to stop it."
LaBarbera was making his fifth straight start in place of Coyotes No. 1 goalie Ilya Bryzgalov, who is out because of a lower-body injury.
LaBarbera had surrendered 15 goals over his previous four starts, but he was sharp against the Stars.
"That 10-day [four-game] stretch was tough," LaBarbera said. "Hopefully, we can take this game and go from there. [Bryzgalov] is the No. 1 one guy. I do my best to fill the role when I can. I'll go back to my normal job. I felt pretty good about the way I've gone."
The Stars pulled goalie Kari Lehtonen for an extra attacker with 1:32 left, but Eriksson missed the net on a close-range attempt.
"We had a number of chances, but sometimes you just get beat by a hot goaltender," Stars coach Marc Crawford said.
Phoenix, which has managed one goal in each of its last three games, went 2-3-1 on its trip.
Lehtonen made 25 saves for the Stars, who had been 10-0-3 in their previous 13 home games.
Turris gave the Coyotes all the offense they needed when he converted the rebound of Shane Doan's shot at 10:46 of the second period.
Martin Hanzal of the Coyotes appeared to score on a deflection at 15:11, but the goal was disallowed after a video review. Officials ruled that Hanzal's stick was above the crossbar, and the Stars went on to kill the penalty with several nice stops by Lehtonen.
Both teams were coming off two-day breaks, and the Stars were lethargic early, partly due to the tight-checking road style favored by ex-Stars and current Coyotes coach Dave Tippett.
"At home, we want to impose the tempo," Stars defenseman Stephane Robidas said. "You want to dictate the game. You don't want to go with the flow and play how the other team plays. We're a much better team when we take charge. When we don't, we're in trouble and that's what happened."
The Coyotes arrived in Dallas on Sunday morning, a change from their routine to allow the players to spend Christmas at home. Tippett liked how his team responded.
"Obviously, it was a tough day," Tippett said. "It's not a regular game day when you have to get up at six in the morning to catch a flight."
Jovanovski played in his 1,000th NHL game. ... Stars D Nicklas Grossman and C Tom Wandell were scratched due to illness, and several of their teammates were also coming down with the same illness. ... Dallas was shut out for the third time this season. Phoenix had its third shutout. ... The Coyotes had allowed six power-play goals the previous two games, but the Stars went 0 for 2 with the man advantage.