Kasperi Kapanen had a goal and an assist for the Blues (31-33-5), who have won two straight and four of six.
"I thought the whole team, though, we did a great job of protecting our slot area and high-danger shots," St. Louis coach Craig Berube said. "[Hofer] was good. Again, solid around the net. No rebounds and things like that, so it's good."
Connor Hellebuyck made 14 saves for the Jets (39-29-3), who were coming off a 3-2 overtime win at the Nashville Predators on Saturday but remained four points ahead of the Calgary Flames for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"We came out of the gate great," Winnipeg coach Rick Bowness said. "Had the forecheck going, we hit the crossbar on a tip, we were jamming the net, we were doing all of the things we had talked about, and then they go down and score. We didn't handle it very well from that point.
"We did have some opportunities; we didn't capitalize on them. They're a big defense, all those guys are big and strong, and we had a tough time battling through them."
Kapanen gave the Blues to a 1-0 lead at 4:04 of the first period when he redirected Nick Leddy's pass to the right post past Hellebuyck. It was his second straight game with a goal.
"I've been happy with him, with his game," Berube said of Kapanen. "He had some good looks in the first period, too. He's been pretty solid all around. Defensively, I said his awareness is good and he plays good 'D.' Offensively, I think he's gaining more confidence as it goes along, to be honest with you."
Later in the period, St. Louis killed off a four-minute power play for Winnipeg to preserve the one-goal lead.
"Whenever you get a power play, you want to at least create some momentum, and we weren't able to do that," Jets forward Nikolaj Ehlers said. "We did have some chances today, but it's the second time in three games that we haven't scored (3-0 loss to the Boston Bruins on Thursday). We need to get more shots, better shots to the net, and we've got to clean up those rebounds."