O'Sullivan beat Jimmy Howard with a wrist shot in the third round of a shootout, and Nikolai Khabibulin stopped Henrik Zetterberg on Detroit's final attempt to give the Oilers a 6-5 victory Thursday night.
The Red Wings overcame a 5-1 deficit to force overtime.
"We had a bunch of goals to start, but unfortunately we didn't continue to play the same way we got those goals," Oilers coach Pat Quinn said. "Detroit's a pretty good team. You can't let them off the hook. We had some fear take over. They started checking and we didn't answer it. We got through it tonight, but it wasn't pretty."
Ales Hemsky had two goals and an assist for Edmonton. Linemate Dustin Penner had a goal -- his ninth of the season -- and three assists, and slumping Shawn Horcoff had a goal and two assists. Jean-Francois Jacques also scored.
"It was nice," Horcoff said. "Penner and Hemmer having been playing at such a level, it's been outstanding. I'd been trying to stay positive."
Edmonton snapped a three-game losing streak to improve to 7-5-1, while Detroit dropped to 4-4-3 with its fourth loss in five games.
Detroit coach Mike Babcock focused primarily on the positives.
"It's one of those give-and-take situations," he said. "It's one of those situations where you can be somewhat happy to battle back the way we did and steal a point, but we still have to be disappointed with not getting the two points.
"It was very important for our team to battle back the way we did and show that kind of grit and determination. As a coach you have to question what they were doing at the start of the game. Overall, we shot ourselves in the foot there. But we challenged our team to respond and they did. It was a real good point from where we began with that terrible start."
Detroit outshot Edmonton 20-6 in the third period, with Eaves tying it a 5 with 7:07 remaining.
Helm's goal was his first in regular-season play. He has six goals in the playoffs. ... Horcoff entered the game with only three points and had been shut out in his last seven games. ... The game was the first of four meetings between the two teams this season. Detroit swept the four-game series last season.