Vejmelka, who signed a five-year contract extension earlier Thursday, allowed two goals in the first 8:49 before stopping the next 29 shots to backstop the comeback.
“We had kind of a slow start tonight, but after the first period, we played a good second and an even better third,” Vejmelka said. “The guys had a lot of great blocks, so this was a big team win.”
Michael Kesselring had two assists for Utah (28-25-9), which has won four of five. Ten players had at least one point in Utah’s first game since a 3-1 loss to the New Jersey Devils Saturday.
“That’s what a team is about,” Utah coach Andre Tourigny said. “What I liked tonight is that every line had a goal. That’s how this team plays.”
Dylan Larkin and Jonatan Berggren scored for Detroit (30-26-6), which has lost four straight. Alex Lyon made 15 saves.
“We just can’t find a way,” Larkin said. “We’ve lost not playing well and we’ve lost playing well. We’re losing in different ways, so we just have to keep looking at the big picture.”
The Red Wings didn’t score in the last 51:11.
“We talk a lot about the race to three (goals), and if you don’t win that, you put yourself in a real tough spot,” Red Wings coach Todd McLellan said. “We didn’t get to three again tonight.”
Nick Schmaltz tied it 2-2 at 13:01 of the second period, scoring a one-timer from the bottom of the left circle off a cross-slot pass from Barrett Hayton on the power play.
Kevin Stenlund put Utah in front 3-2 at 2:55 of the third period, picking up a loose puck at the right face-off dot and beating Lyon with a snap shot.
“It’s a 2-2 game there and we had a lapse in our end and they get one,” Larkin said. “We just can’t do that at that point in the game.”