Rookie Jason Chimera led a two-on-one 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 goaltender Curtis Joseph to raise Edmonton's record against the defending Stanley Cup champions to 2
Anson 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.
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.