Brewer scored 1:42 into overtime to give the Edmonton Oilers a 4-3 victory over the Red Wings.
Rookie Jason Chimera led a 2-on-1 before crossing the Detroit blue line and dropping a pass for Brewer. Selected to participate in his first All-Star Game, Brewer fired a wrist shot over the glove of former Oilers goaltender Curtis Joseph to raise Edmonton's record against the defending Stanley Cup champions to 2-0-1.
"I saw the puck turn up the ice and was going as a trailer," Brewer said. "But Chimera hit the brakes and left me the puck, so I just shot it as hard as I could."
"We had a chance to win in overtime with an odd-man rush and they turned the puck around and Brewer made a great shot to win it," Detroit center Kris Draper said. "(Anson) Carter had a big game for them and they made the most of their chances. Seems like every time we make even a little mistake lately, it ends up in the back of our net."
Carter scored twice and rookie Jani Rita netted his first NHL goal for the Oilers, who had dropped three of their previous five games.
Jussi Markkanen stopped 36 shots in place of Tommy Salo, who was relegated to backup duty due to tonsilitis.
"Five-on-5, we were pretty good all night," Markkanen said. "These are two huge points and now we can look forward to our next couple of home games."
Brett Hull reached the 20-goal plateau for the 16th consecutive season with a power-play tally in the second period, leaving him one from becoming the sixth player in NHL history to score 700 goals.
Igor Larionov and Draper also tallied for Detroit, which has lost three of four.
Carter opened the scoring at 5:24 of the first period with his 18th goal. Mike York got a feed from Carter in the right faceoff circle and unleashed a shot that never found the net. From the right side, Carter tracked down the puck in the low slot and fired a turnaround shot past Joseph.
"To be able to come out and play well against the Stanley Cup champs is a big confidence boost," Carter said. "Playing with York and T-Bone (Todd Marchant) is really good. Those guys fly up and down the ice and I'm just trying to keep up."
Recalled from the minors Friday due to a rash of injuries, Rita gave Edmonton a two-goal cushion midway through the period.
Marty Reasoner grabbed a loose puck in the right corner and dished to Daniel Cleary, who spotted Rita on the doorstep. Playing just his fourth NHL contest, the 21-year-old Finn wrapped a backhander around a defenseman and past Joseph at 10:42 to put the Oilers ahead, 2-0.
"Cleary made a nice pass to me in front and I just shot the backhand," Rita said. "I didn't even see it go in because I had my back to the net. I didn't know it was in until I heard the crowd going wild. It'll be a nice memory for me. I've seen (the Red Wings) on highlights for years, and scoring my first goal against a great goalie like Curtis Joseph is special."
Detroit erased the deficit in a 6 1/2-minute span of the second period.
While on the power play, Larionov gathered the rebound of Hull's slap shot from the right circle and tried to stuff the puck behind Markkanen. After his first shot was stopped, the 42-year-old Russian made good on his second try at 7:34 for his fourth tally of the season.
Hull knotted it with a power-play goal at 14:05, slapping a one-timer from the left circle past Markkanen's stick side.
Draper gave the Red Wings their first lead 3:25 into the third. With rookie defenseman Dmitri Bykov in the penalty box for slashing, Kirk Maltby intercepted a pass in his own zone and sent Draper on a breakaway. After faking a backhander, Draper slipped the puck inside the left goalpost from just above the crease for his seventh career shorthanded goal.
But Carter scored his second of the game 30 seconds later to draw Edmonton even.
York carried down the left wing and fed Carter, whose shot from the slot bounced off a sprawled Joseph and into the net for his third two-goal effort of the season.
"We finally got a power play in the third and they chip one by us and Draper scores on a breakaway," said Craig MacTavish, who recorded his 100th win faster than any coach in Edmonton history. "It was great that Anson answered right back, and we finally got our first break of the hockey game in the overtime and won the hockey game with it."
"Usually, when you score a shorthanded goal, it disheartens your opponent," Detroit coach Dave Lewis said. "But Edmonton didn't let that happen. They bounce right back and wound up with a gutsy win for their efforts. They deserved what they got tonight, they made the most of their opportunities."