Raffi Torres scored 1:51 into the extra session, and Edmonton beat the Red Wings 4-3 on Thursday night to end their nine-game winning streak.
"You knew it was going to happen sooner or later," Detroit goalie Chris Osgood said.
Shawn Horcoff had a goal and an assist for the Oilers. Ryan Smyth and Fernando Pisani also scored, and Chris Pronger added three assists.
"It's huge for us. We knew these guys were experienced," Smyth said. "And with the record they've got, it is something we want to build on."
Tomas Holmstrom scored twice for the Red Wings (12-1-1-0). Jason Williams had a goal and an assist, and Pavel Datsyuk had two assists. Detroit's nine-game winning streak tied a franchise record - the Red Wings' only other loss was a 4-1 defeat in Toronto on Oct. 1.
"You like to think the team will get a little casual," Oilers coach Craig MacTavish said. "But that wasn't the case tonight."
Torres tipped in a pass from Steve Staios after a give-and-go for his ninth goal of the season.
"I kind of gave it to him, left it," Torres said. "He made a great pass and I got lucky."
Williams' power-play goal 8:05 into the third period tied it at 3 for Detroit. He scored on a one-time slap shot from the top of the left circle off a pass from Datsyuk.
"Tough team to protect a lead against," MacTavish said.
Pisani gave Edmonton a 3-2 lead 4:11 into the third when he tipped Pronger's shot from the point out of mid air.
"I thought we were really going to play tonight," Red Wings coach Mike Babcock said. "At times we did."
The score was tied at 2 going into the third period after both teams scored on the power play in the second.
Smyth gave Edmonton a 2-1 lead when he tapped a cross-crease pass from Ales Hemsky into the empty side of the net at 5:37. Holmstrom's second goal, a one-timer from the bottom of the right circle off a pass from Datsyuk, made it 2-2 at 8:43.
Horcoff opened the scoring 4:34 into the game when his shot from the slot trickled through Osgood's pads. Holmstrom tied it at 7:44, when he intercepted Cory Cross' pass in the left circle, skated across the slot and put a backhand shot over Jussi Markkanen's shoulder.
Detroit was without G Manny Legace (sprained knee) and D Jason Woolley (groin). ... Edmonton was without C Michael Peca (concussion). ... Detroit D Mathieu Schneider returned after missing a game with a sore groin. ... Cross left the game after the second period with a sprained left knee.