Gagner made it 2-0 at 10:38 of the third period with a slap shot from the top of the right circle, and Barron extended it to 3-0 at 13:43 with a one-timer from the low slot.
"You're always in it, but they just kind of hemmed us in there," Blues forward Brayden Schenn said. "I don't think we deserved to win it tonight by any means. We were in it, I guess, until midway through the third period, but I don't think we deserved to win it. It wasn't our best. We'll flush it out and get ready for our next one."
Perfetti shot into an empty net at 18:26 for the 4-0 final.
"I thought we did a great job tonight of getting to the net, of not playing to the outside," Arniel said. "We played a lot more on the inside of the offensive zone, and we got rewarded for it."
NOTES: St. Louis was shut out for the first time in 109 games. … Perfetti has five points (two goals, three assists) on a four-game point streak… Hellebuyck's shutout was his first this season and 29th in the NHL. … The Jets are 6-0-1 in their past seven games against the Blues. … Prior to the game, the teams observed a moment of silence in memory of the victims of the shooting at Central Visual and Performing Arts High School in St. Louis.