Paul Stastny scored twice, and Malcolm Subban made 29 saves for the Golden Knights (42-30-6), who have lost four in a row (0-3-1).
"For sure [it's bittersweet]," Golden Knights forward Mark Stone said on clinching despite losing. "I think every team's goal at the start of the season is to make the postseason. We're obviously excited to be in there, but we want to play better hockey."
The Wild (36-33-9) remain four points behind Colorado for the second wild card into the playoffs from the Western Conference. Minnesota won for the fourth time in 13 games (4-6-3) and improved to 3-0-0 all-time at T-Mobile Arena.
Eric Staal had a goal and an assist, and Devan Dubnyk made 35 saves for Minnesota, which is 14-6-2 in its past 22 road games.
"I thought we had a good mindset," Dubnyk said. "You've got to have that sense of urgency and understanding it's a must-win game, but we can't change what we're doing. We all know what we need to do to be able to play, and we did that."
Greg Pateryn scored his first goal for the Wild at 2:12 of the first period for a 1-0 lead. It was Pateryn's 76th game after signing as a free agent July 1. He had not scored in 131 games, since Dec. 3, 2017, when he was with the Dallas Stars.
Staal made it 2-0 on the power play at 19:38 when he deflected Jason Zucker's shot from the slot.
Kevin Fiala scored on a rebound on the power play at 11:22 of the second period to increase the lead to 3-0.
Stastny made it 3-1 on a rebound at 18:00, and he cut it to 3-2 at 8:52 of the third period.
"You look at the third period, I think we were really dominant, but you can't get behind in this league," Stone said. "It's too good of a league to give the other team goals. We can't put ourselves in those situations."
