Robert Thomas scored short-handed for St. Louis to cut it to 5-3 at 16:00 of the third period, and Dylan Holloway made it 5-4 with 15 seconds remaining with Joel Hofer pulled for the extra attacker.
Kirill Kaprizov had a goal and two assists, Danila Yurov also scored and Jesper Wallstedt made 21 saves for the Wild (5-2-1), who won for the third time in four games (3-1-0).
Quinn Hughes had two assists to extend his season-opening streaks for points (two goals, 10 assists) and assists (10 assists) to eight games.
“I thought we played a really strong, collective team game,” Minnesota coach John Hynes said. “We played organized. We were stingy, highly competitive. Our detail was good.”
Thomas had a goal and an assist, Mason McTavish scored and Cam Fowler had three assists for the Blues (3-3-1), who had points in three straight (2-0-1). Hofer made 33 saves.
Despite battling back to make it a one-goal game in the end, St. Louis didn’t contain Minnesota’s top line well enough, especially in the second period, coach Jim Montgomery said.
“They’re very dangerous, and they showed us why they’re so dangerous,” Montgomery said. “And we made it too easy for them. I did like our fight to come back and just to try and prevail in the game.”
Jonatan Berggren’s power-play goal gave the Blues a 1-0 lead 1:45 into the game, finishing top shelf on the backhand.
Boldy tied it 1-1 at 7:31 with a quick slap shot during a 5-on-3 advantage.
Yurov put the Wild ahead 2-1 at 11:17, scoring from the high slot off the rush on a pass down low from Maxim Shabanov.
McTavish tied it 2-2 at 4:57 of the second period, but Boldy responded just 27 seconds later with his second goal to put the Wild back in front 3-2, with Joel Eriksson Ek recording his second assist on the play.
“Their top line was really good all night,” Thomas said. “We were chasing them around. They made a ton of plays. We’ve got to do a better job. We knew how dangerous they were -- we let them have an easy night tonight.”
Kaprizov extended it to 4-2 at 8:47 with his ninth goal of the season. He passed the puck to Hughes, then went to the front of the net for the tip-in goal.
“The more reps and games we get together, the more we're just going to be reading off each other,” Hughes said of playing with Kaprizov and Boldy. “And I feel like we're getting to a place now where we're in a good spot with that. And it's just so fun, so fun playing with them.
“I feel like when we're out there together, we just tilt the ice.”