Getzlaf scored in the third round of the shootout after goaltender Jonas Hiller denied two of three Dallas shooters and the Ducks beat the Stars 2-1 on Saturday night.
Dallas' Mike Ribeiro hit the post with his third-round attempt, and Getzlaf ended the game with a forehand shot from the slot that caromed off the post and past Turco.
Getzlaf has gone against Turco many times before, and Getzlaf knows Turco likes to come out of his net and challenge shooters.
"I know Marty a little bit, how he likes to come out," Getzlaf said. "I thought I'd slow it down a little bit to throw his timing off so he couldn't just back into the net."
The Stars were beaten in their first game since a knee injury ended captain Brenden Morrow's season.
Morrow sustained a torn knee ligament with about six minutes left in Thursday night's 6-3 loss to the Chicago Blackhawks. Morrow, who has scored 173 goals in nine seasons with the Stars, will be out about six months after surgery that's yet to be scheduled.
Perry scored in regulation for the Ducks, who had lost six of their previous eight.
But the Ducks earned three of four points on the road in a 24-hour stretch after Friday night's 3-2 overtime loss at St. Louis.
"We're not going to get too high with a shootout win," Anaheim coach Randy Carlyle said. "You want to take that workmanlike attitude into the next game to try to establish our identity. We want to get back playing our grinding type of hockey."
Loui Eriksson had the regulation goal for the slumping Stars, 2-5-3 in their past 10 games.
Stars coach Dave Tippett hasn't been pleased with his team's recent effort, so Saturday night's tight-checking style was an encouraging sign.
"We had heart and we had lots of compete in us," Tippett said. "We would certainly like to get that extra point. But we had a lot of guys that played hard."
Perry's sharp-angled power-play goal at 5:37 of the opening period on his team's first shot gave Anaheim the early lead. Dallas' Sean Avery, who had nine first-period penalty minutes, was in the penalty box while Perry scored.
The first period ended with three fights and 46 penalty minutes.
Eriksson converted Trevor Daley's centering pass at 10:09 of the second period to even the score at 1.
The Ducks thought they'd gone in front 2-1 on another Perry power-play goal at 15:01 of the second period. But after a video review, officials ruled that the net was off its pegs before the puck crossed the goal line and the goal was disallowed.
The Stars, who started the night having allowed the most goals in the Western Conference, at least did a better job defensively.
"The way things have been going, it goes without saying that there were some positives tonight," Turco said. "We're emphasizing the little things and it's nice to get the point, but we really wanted the win."
Turco said the team will greatly miss Morrow.
"I'm used to having him in the lineup making a difference, pulling the guys along," Turco said. "There's not too many guys in the league you'd miss as much as Brenden Morrow. We've got to pick up the slack."
Center Brendan Morrison was a healthy scratch for Anaheim. In 21 games, Morrison has two goals and two assists with a minus-5 rating. ...The Stars are 9-2-3 their past 14 regular-season meetings with the Ducks.