Clayton Keller scored twice, and Karel Vejmelka made 34 saves for Utah (12-11-5), which has earned a point in six of its past seven games (4-1-2).
“It's a tough game, they're a good team,” Utah coach Andre Tourigny said. “We could feel we're not as energetic as we normally are. So, having that pushback late in the game, even if the guys were tired, I think that was huge. Unfortunately, we could not close the deal.”
Kevin Stenlund gave Utah a 1-0 lead at 13:46 of the first period, burying a one-timer five-hole on Gustavsson off a pass from Michael Carcone.
Utah appeared to extend the lead at 8:24 of the second period on a shot from Dylan Guenther, but Minnesota challenged the play for offside, and the call was reversed after a video review.
Khusnutdinov tied it 1-1 at 14:25, beating Vejmelka blocker side on a breakaway after intercepting a blind pass from Mikhail Sergachev at the defensive blue line.
Kaprizov scored 36 seconds later to give the Wild a 2-1 lead. His shot trickled past Vejmelka on another breakaway after Johansson poked the puck away from Olli Maatta.
Keller tied it 2-2 with a power-play goal at 4:42 of the third period, beating Gustavsson glove side with a wrist shot from the right circle.
Johansson responded back for Minnesota to make it 3-2 at 5:39. Vejmelka thought he had covered the puck, but it trickled behind him, and Johansson knocked it in before Maatta could help out his goaltender.
“I feel like we have all four lines going,” Johansson said. “Everyone's buying in and everyone's doing the work, so it's fun to see.”