Detroit answered 1:48 later on a goal by Emmerton. Brunner then pushed the lead to 4-1 with his fifth goal of the season.
Valtteri Filppula added an unassisted goal in the third, giving the Red Wings five different goal scorers.
"Anytime you get depth in scoring, it's a positive thing," Detroit coach Mike Babcock said. "I thought our discipline was pretty good. We responded and we really pushed."
Drew Miller had two assists for the Red Wings.
St. Louis won six of its first seven games before dropping three in a row. The Blues have lost their last two home games by a combined 11-2.
"When you have players (playing) under the bar, it's tough to win hockey games," coach Ken Hitchcock said. "We're cheating all over the ice. Our team game is not good right now."
The struggling Elliott has given up nine goals on 40 shots in his last two games.
"Goals are going to go in. The best goaltenders in the world let in goals," he said. "So you can't be too hard on yourself. We'll figure it out. It's just a matter of time."
NOTES: St. Louis D Wade Redden appeared in his 1,000th NHL game. ... Detroit LW Henrik Zetterberg extended his point streak to seven games with an assist on Brunner's goal. Zetterberg has 12 points in his last seven contests. ... Detroit has scored in the first period in just three of 10 games. ... The teams played three times in the first 10 games and will meet two more times this season. ... St. Louis has scored at least one power-play goal in its last four games. ... Mrazek complied a 16-7-3 record in the minors.