Jimmy Howard stopped 26 shots in his return after missing two games because of a bruised right kneecap, and Patrick Eaves, Todd Bertuzzi and Jakub Kindl -- with his first NHL goal -- scored in regulation to help Detroit snap a three-game road losing streak.
The Red Wings blew a three-goal lead before rebounding for their ninth overtime win in 15 chances.
Helm scored his first winning goal of the season by zipping up ice to create an odd-man break.
"Speed is the biggest part of my game and I've got to utilize that every chance I get," Helm said. "I was able to get up ice as quick as I could and able to find a way to put it in."
Helm excels in the open ice, according to Detroit coach Mike Babcock.
"If you go through all the 4-on-4 overtime wins that we have, he seems to be involved in all of them," Babcock said. "He's dangerous in situations like that, no question about it."
Backes tied it with 5:46 left in regulation, beating Howard from close range.
Oshie cut it to 3-1 midway through the second, and Berglund scored at 6:35 of the third. Oshie returned to the lineup Tuesday night in a victory over Los Angeles after missing 31 games because of a broken ankle.
"Obviously, you want to get two points every night," Oshie said. "But we battled back. You have to learn from this and not put ourselves in a hole like this -- especially against a team like Detroit."
Kindl gave the Red Wings a 3-0 lead at 9:50 of the second. The 19th overall pick in the 2005 draft, he was appearing in his 22nd NHL game and 19th of the season.
"It feels good, I'm not going to lie," Kindl said. "It was a little lucky."
Eaves opened the scoring at 12:25 of the first period with his fourth goal in eight games. Bertuzzi and Kindl scored in a 2:16 span midway through the second period.
Babcock was pleased with the way his club rebounded after a wasting a three-goal lead on the road.
"We got back to playing the way we knew we could," he said. "We did a lot of really good things. This was a good win for us.
Howard made several key saves late in regulation. He did not appear bothered by the knee injury, which was expected to sideline him for up to two weeks.
"I felt pretty good to be honest," Howard said. "It was one of those things where we didn't let up, I just think [St. Louis] woke up. They started getting pucks in deep."
The Red Wings have won three of four games against the Blues this season. ... Hudler added three assists for the Red Wings. ... St. Louis center Andy McDonald, sidelined by a concussion since Dec. 4, skated for the first time over the past two days. "There was some progression -- each day gets better," McDonald said. ... The Red Wings have been outscored 15-8 in the first period over their last 10 games. ... St. Louis is 10-2-2 with Oshie in the lineup. ... Howard has won his last four starts against St. Louis. ... Detroit is 5-1-1 when Bertuzzi scores. ... The Blues have sold out all 25 home games this season.