The Oilers trailed twice but pulled each time. Alex Hemsky scored late in the second period and Andrew Ference connected late in the third to force overtime.
Edmonton succeeded on both of its attempts in the tiebreaker; Jordan Eberle scored in the first round by slipping a shot inside the near post. Rich Peverley scored Dallas' lone goal in the second round. The game ended when rookie forward Alex Chiasson lost the puck on Dallas' third attempt.
"I think in order to be a good hockey team, you have to show some resiliency because things aren't always going to go your way," said Oilers forward Ryan Jones, who assisted on Hemsky's goal. "You have to be resilient or you just find yourself losing hockey games that you shouldn't. We showed that tonight."
The Oilers won despite losing starting goaltender Ilya Bryzgalov to an upper-body injury late in the second period. Bryzgalov stopped 28 of 29 shots in 36:19. However, with 3:41 left in the second, he and Dallas' Ryan Garbutt, who had both goals for the Stars, collided in front of the net.
Bryzgalov was holding his head while lying on the ice and left the game.
"He's got an upper-body injury that we're going to have to reassess in the morning. I've been upfront with you guys," Oilers coach Dallas Eakins told the media. "I'm not being upfront now. I've got to keep this under wraps until we check him out a little further."
Bryzgalov was replaced by Devan Dubnyk, who stopped 15 of 16 shots to earn his seventh win.
"It's tough right at the start when you first come off the bench. Everything is dry and the ice is beat up a bit. It's always a weird feeling, especially when there is a faceoff in your end right away, but that's part of the job," Dubnyk said. "You want go in there and be real simple and try to get hit with a couple, and then when you come in for the intermission you go through the routine and it feels like a normal period going out for the third."
Garbutt scored a shorthanded goal in the second period, his fourth goal of the season, beating Bryzgalov with a backhander at 11:36 after stealing the puck from Oilers defenseman Denis Grebeshkov near the Edmonton blue line.
The Oilers have allowed five shorthanded goals this season, tying them with the Winnipeg Jets for the most in the League. Dallas was shorthanded after Jordie Benn was called for slashing, his first penalty of the season, at 9:38.
Garbutt scored again at 3:45 of the third, beating Dubnyk with a wrister from the low slot.
Edmonton tied it for a second time at 14:53 when Ference scored his second of the season after a slapper from the point trickled through Lehtonen (30 saves) to make it 2-2.
Hemsky made it 1-1 with his fifth of the season five seconds before the second intermission. Jones gained possession after a hit on Chiasson near the right boards, then then sent a pass towards the Dallas net that Hemsky quickly tapped in for the equalizer.
"It was just kind of a loose puck battle and I wanted to go in hard just to win it," Jones said. "It was kind of a collision between the two of us along the boards. The puck squirted out behind us and I just turned and threw it there. It was a big goal for us late in the second to tie it up."
Stars center Tyler Seguin missed the game with concussion-like symptoms. In his absence, coach Lindy Ruff shuffled all but his fourth line, keeping the trio of Garbutt, center Vernon Fiddler and left wing Antoine Roussel together. That move paid off.
"He's day to day with concussion-like symptoms," Ruff said of Seguin. "He'll make the trip [to Chicago]. This had nothing to do with earlier in the week when he had a muscle strain. This was a hit that just caught him right. He went through the protocol. The doctor did the testing and ruled him out."
One positive for Ruff was the performance of rookie defenseman Jamie Oleksiak, Dallas' top pick (No. 14) at the 2011 NHL Draft, who was making his season debut. Oleksiak had big shoes to fill on Dallas' first defensive pairing alongside Brenden Dillon after veteran Stephane Robidas was lost for at least four months with a leg fracture in a shootout loss on Friday to the Chicago
The 6-foot-7 defenseman more than held his own in his 17th NHL game.
"He did a nice job against their speed. He was very good," Ruff said.
The Stars had a two-man advantage for nine seconds late in the first, but failed to convert. Dallas was 0-for-4 on the power play in the game, making the Stars a League-worst 1-for-37 with the man advantage at home.
Dallas outshot Edmonton 18-9 in the opening period and 45-32 overall.