DALLAS -- The Edmonton Oilers made the most of limited offense and both parts of their goalie tandem.
"It's nice to get a win," Perron said, "mostly with the shot total that was tonight (Dallas 45, Edmonton 32). We greased one out."
Dubnyk stopped two of three shots in the tiebreaker. Dallas' Kari Lehtonen failed to make a save in the shootout after stopping 30 shots through the first 65 minutes.
"Things weren't really going our way for the first half of the game, so you knew there was going to be some shots," Dubnyk said. "I thought we responded pretty good to it."
Ryan Garbutt scored two goals, including a short-handed tally that gave Dallas a 1-0 lead in the second period. He also put the Stars ahead in the third.
"It's obviously pretty important to have good shootouts," Garbutt said. "We've had (Rich) Peverley scoring goals in the last two games, but we need more guys stepping up when we've got the opportunity."
Garbutt nearly had a hat trick but he was stopped on a breakaway attempt by Bryzgalov with 3:41 left in the second. Garbutt collided with Bryzgalov, who left with an upper-body injury and didn't return.
"That line and (Garbutt) have played well," Dallas coach Lindy Ruff said. "He had eight shots and he skated well. He could have had four goals tonight. He's creating them himself with his speed."
Bryzgalov, who made 28 saves, trailed 1-0 when he came out.
Edmonton coach Dallas Eakins praised both of his goalies.
"Both those guys, and especially (Dubnyk) coming in the way he did, they were a real catalyst for our team," he said. "To come in off the bench, it's never easy. You've been sitting there for a long time, and then to make especially those saves in tight, that kept us going.
"When your goaltending's good it allows you to hang around in the game. They could have easily been first or second stars or second and third, which would have been maybe a first in the NHL."
The Oilers improved to 2-1 in shootouts. The Stars dropped to 3-3, including two straight losses in the tiebreaker.
Ruff said there was a difference between Friday's 2-1 loss to Chicago, which owns the NHL's best record, and Sunday's defeat against the seventh-place team in the Pacific Division.
"This was a lot more frustrating," he said. "There was glorious opportunities to put it away. We've got to bear down better and make sure we finish on some of those opportunities."
Edmonton's other shootout win was on Oct. 7, when Eberle scored the deciding goal against New Jersey.
Garbutt put the Stars in front in the second period when he stole the puck near the Edmonton blue line, skated in alone on Bryzgalov, and put a backhander into the upper right corner of the net.
The unassisted goal came at 11:37, just 1 second before Dallas' Jordie Benn was to come out of the penalty box. It was the Stars' second short-handed goal this season.
Garbutt has five goals this season, and 10 in 76 NHL games.
Dallas had 18 shots in the first period, but couldn't score against Bryzgalov.
In the second, the Oilers finally broke through against Lehtonen, who had shut them out in Edmonton on Nov. 13.
Jones sent a pass from the top of the right circle to Hemsky in front. Lehtonen stopped Hemsky's first attempt, but Hemsky poked in the rebound. The Oilers had been scoreless in 108 minutes against Lehtonen.
"It was just kind of a loose puck battle and I wanted to go in hard just to win it," Jones said. "The puck squirted out behind us, and I just turned and threw it there.
"It's kind of been my mentality all throughout hockey, just get pucks there. It was a big goal for us late in the second to tie it up."
Eakins wouldn't elaborate on Bryzgalov's injury. "I've got to keep this under wraps until we check him out a little further," he said. . Center Tyler Seguin, leading Dallas with 12 goals, missed his first game this season because of concussion-like symptoms resulting from a hit during Friday's game against Chicago. . The Stars failed to score on four power plays, including 9 seconds with a 5-on-3 advantage late in the first period. Dallas is the only NHL team with fewer than 10 power-play goals. Seguin has two of the Stars' nine. The team is 1 for 37 at home and 9 for 86 overall. . The Oilers were 0 for 6. Their two first-period power plays followed Stars bench minors for too many men on the ice. . Defenseman Jamie Oleksiak played and started his first game for Dallas this season, and was credited with two blocked shots and three hits. He was recalled from Texas of the AHL when Stephane Robidas went on injured reserve.