They'll meet Sunday night in Dallas as each begins trying to climb out of their respective cellars.
Dallas' position in the Central Division is the more correctable of the two. The Stars (12-9-3) have 27 points, which would put them near the middle of every other division. The Oilers' 18 points, on the other hand, are the fewest in the Western Conference.
The Stars are coming off a 2-1 shootout loss to Chicago on Friday in which they lost defenseman Stephane Robidas to a broken leg. He had surgery Saturday morning and will miss at least four months. Losing him creates further defensive issues for Dallas, which is already in the bottom third of the NHL in goals against with a 2.83 average.
"It was heartbreaking," goaltender Kari Lehtonen told the team's official website. "He is the one guy who never stays down. I saw his face and knew something really went bad. It was tough to play the rest of the second period. ... It kind of sucks right now. He'll work hard and come back. He's a huge part of this team."
The 11-round shootout was the longest in the NHL in nearly three years.
"That was one hell of a hockey game," Stars coach Lindy Ruff said. "When you lose one like that it hurts, but when you get a point and you played them as tough as you did, you can take something away from that."
Lehtonen made 25 saves through regulation and overtime before stopping nine shootout chances. The Stars' veteran goalie earned his only shutout of the season Nov. 13 at Edmonton. He's 10-3-0 with a 2.08 goals-against average in his career against the Oilers.
Including the 3-0 victory over Edmonton earlier this month, the Stars have won 12 of 14 against the Oilers dating to Jan. 22, 2010.
A little help from the power play could make improving on that run a bit easier. Against Chicago, the Stars went a third straight game without a power-play goal. They haven't scored on their last nine chances, and their 11.0-percent mark on the season is among the worst in the league.
The Oilers (8-17-2) are also trying to avoid a losing streak after Friday's 4-2 defeat at Columbus. They fell behind 4-0 before getting third-period goals from Sam Gagner and David Perron.
"We weren't ready to go right out of the gate," Oilers coach Dallas Eakins said. "Even though I thought we slowly fought back, there was just a lot of head-shaking moments on our bench. Not only from the coaches but the players themselves."
Edmonton had been enjoying its best stretch of the season with four wins in its previous five games.
"It's frustrating when you get a win in Nashville and come out like this tonight," forward Jordan Eberle told the team's official website. "Plain and simple, we had to win this game and we didn't."
Ilya Bryzgalov made his second start in net for the Oilers after being signed Nov. 8, but he was replaced at the start of the third period by Devan Dubnyk. Bryzgalov earned a 33-save shutout Thursday at Nashville in his first start of the season.