Logan O'Connor sent a pass from the right wall off the left wall boards, and Helm came in and stepped into a shot that got through traffic and past Ville Husso's glove.
"I think early on up the ice, we're kind of in a set forecheck, we let their D get by us and carry the puck up the ice, created a little bit of an odd-man rush, made a play to the weak side," St. Louis coach Craig Berube said. "They shot it, went through some people and it went in. But up ice, we could have done a better job."
The Avalanche won the best-of-7 series 4-2 and advanced to the conference final for the first time since 2002. They will face the Edmonton Oilers in Game 1 on Tuesday.
J.T. Compher scored twice, and Darcy Kuemper made 18 saves for Colorado, the No. 1 seed from the Central Division.
The Avalanche had been eliminated from the playoffs in the second round the past three seasons.
"It means a lot," forward Nathan MacKinnon said. "I think you really have to enjoy the journey. That's the most important thing we're going to look back on is the journey of getting to this point. There will only be four teams soon and obviously the job's not finished, but that's a great accomplishment for us.
"There have been some dark times. Nice to get over this hump, for sure. Definitely felt like we outplayed them this series. Just some tough periods in our end, but even tonight we played a great 60 minutes. Some key saves by 'Kemps', big block by Josh Manson] and obviously big goals by 'Comph' and 'Helmer'. I thought we outplayed them for the majority of the series, and definitely tonight, and we deserved a good bounce there at the end."
***[[Complete Avalanche vs. Blues series coverage]*
Husso made 36 saves, and Justin Faulk and Jordan Kyrou scored for St. Louis, the No. 3 seed from the Central.
"Obviously the game, we had a chance to take it," Blues captain Ryan O'Reilly said. "I thought 'Huus' gave us a chance, he made some huge stops, gave us a chance all game. I thought we started a little slow, which hurt us. That was kind of the feeling that we had all series at home. We didn't play the way we needed to here, which made it difficult to win. Lost every game at home here … just very disappointing."