Jake Allen made 20 saves, and Vince Dunn scored in the third period for the Blues.
"It's tough, it's the first game and certainly not going to go overboard here with what we're feeling," St. Louis coach Mike Yeo said. "Obviously it's disappointing. I think that there's a lot to learn from the game about our group and playing against a good team like that and what goes into winning games. I think we had some opportunities and didn't capitalize."
Laine scored a power-play goal to give the Jets a 1-0 lead at 4:01 of the first period, a shot that was deflected by Blues defenseman Colton Parayko.
"I think it hit a stick," Laine said. "I'm not a preseason guy, and when the season starts, I'll start scoring. I felt really good during the game. I was able to create some good chances. I think it was a pretty good first game."
Winnipeg scored three third-period goals in a 1:44 span on consecutive shots.
Lowry's shorthanded breakaway made it 2-0 at 5:51; Wheeler scored at 6:55 to make it 3-0; and Connor scored at 7:35 to make it 4-0.
"We kind of beat ourselves there," Blues captain Alex Pietrangelo said. "Yeah, we gave up the shorthanded goal, but it's the ones after that that we have to grab control of. I thought we were good up to that point. We had a lot of really good looks, especially on the power play. When you're not capitalizing, can't make those kinds of mistakes."