Dallas (43-32-7), which went 5-1-1 in its final seven games, will play the Nashville Predators, who won the Central Division, in the first round. Ben Bishop made 24 saves for his NHL career-high seventh shutout of the season, and Tyler Seguin scored twice.
"The fun begins now," Stars coach Jim Montgomery said.
WATCH: [All Wild vs. Stars highlights]
Alex Stalock made 41 saves for Minnesota (37-36-9), which went 4-9-1 in its final 14 games.
"It was a tough one tonight for sure," Wild forward Eric Staal said. "There's a certain level you need to be at to be competitive in this League, and we weren't at it besides [Stalock]."
The Wild, who were eliminated from playoff contention on Tuesday, will miss the postseason for the first time since 2012.
"I thought even at the deadline there we made a lot of moves and we brought on a lot of new faces," Staal said. "I still thought we had a chance to work our way to a playoff spot. Unfortunately, we weren't able to get enough guys going to be able to push for that last spot. It's disappointing, obviously, to be left to play for nothing, and we looked like that tonight."