DALLAS -- Shawn Horcoff implored his coach to give him a turn in the shootout.
He didn't disappoint.
Oilers coach Pat Quinn used his most skilled shooters in the first four rounds, then turned to Horcoff, who rewarded his coach by improving to 6 for 10 in career shootout chances.
"Horcoff wanted the shot," Quinn said.
Edmonton rallied from a two-goal deficit in the first period to send the game to overtime, and Patrick O'Sullivan gave the Oilers the early edge by converting in the first round of the shootout.
Loui Eriksson evened the shootout for Dallas in the third round, but Dallas' Brenden Morrow hit the goal post with a shot in the fifth round to set the stage for Horcoff's winner that went in off the stick of Stars goaltender Marty Turco.
Turco had poke-checked the puck away from two previous Edmonton shooters, and Horcoff took notice.
"I have the same routine at the blue line where I make a decision on where I'm going to go," Horcoff said. "I thought about going high, but then I thought he was going to poke-check, so I went five-hole. He has his stick in an area where he can make a poke-check."
Shootouts haven't been good for the Stars, who fell to 1-6 in the tiebreaker this season and have been involved in a league-high 11 overtime games.
"The shootout foiled us again," Dallas coach Marc Crawford said. "This was a game that probably falls more in the category of we shouldn't have ever let it get to a shootout."
The Oilers entered the game 3-21-1 in their previous 25 games in Dallas before picking up two points on this trip.
Ladislav Smid broke a 151-game goal-scoring drought to tie it late in the third period, and Lubomir Visnovsky added a goal for Edmonton. Deslauriers stopped 33 shots in his eighth straight game while starter Nikolai Khabibulin recovers from a back injury.
Dallas seemed headed for the victory with a 2-1 lead and the clock winding down, but Smid scored his first goal of the season and fourth of his career with 3:07 left to tie it on a shot from the right circle that got through Turco's pads.
"It was a great feeling, especially because it helped the team come back," Smid said. "I didn't know it was 151 games. If I counted, I would be frustrated."
The Stars dominated the opening period, building a 2-0 lead with an 18-10 shots advantage.
Benn put Dallas on top at 15:51, knocking the rebound of Mike Ribeiro's shot past Deslauriers.
Neal scored his team-best 13th goal from the slot off Brad Richards' setup at 19:29 to make it 2-0, Neal's second in as many games.
Edmonton narrowed the gap to 2-1 at 2:15 of the second period when Visnovsky's blast from the right point got through a screened Turco.
Dallas is 4-0-2 in its last six games at home, but the Stars bemoaned the loss of an extra point on Saturday.
"It was 2-0 and then 2-1 with 3 minutes left," Ribeiro said. "I think we should have been able to close it out. When you don't have the lead and you come back and tie the game and lose in the shootout, you're like, 'OK, we got the point.' But when you have the lead and then lose in the shootout, it's a little bit harder."
The Oilers went to OT for the seventh time this season. ... Edmonton was on the third stop of a six-game trip. ... Dallas D Karlis Skrastins was scratched due to a deep cut in his right index finger sustained in the win over Anaheim on Thursday night and is day to day. He was replaced by Jeff Woywitka. ... RWs Ales Hemsky (shoulder) and Fernando Pisani (colitis) are out for Edmonton.