WATCH: [All Rangers vs. Wild highlights]
"The message (in the second intermission) was the same as I've been telling them lately: 'Do you want to keep on going on like this and getting 40 shots on a goal a game, having to fight. You get a 3-0 lead and fight to keep it. It's not the right way to play. Play the right way and something good will probably happen to you,'" Wild coach Bruce Boudreau said. "... Getting a 3-0 lead, it seems to me that we say, 'OK, we've got three, let's stop right there.'"
The Wild (31-19-6, 68 points), who allowed four shots on goal in the third period, lead the Los Angeles Kings and Anaheim Ducks by three points for the second wild card into the Stanley Cup Playoffs from the Western Conference.
Defenseman John Gilmour scored his first NHL goal for the Rangers, who lost for the first time in three games.
"We beat ourselves," said goalie Henrik Lundqvist, who made 26 saves. "It's tough, especially the way we played for 45-50 minutes. That's the way we need to start, and it's on all of us."
New York (27-25-5, 59 points) is four points behind the Carolina Hurricanes for the second wild card into the playoffs from the Eastern Conference.
Eric Staal scored unassisted to give Minnesota a 1-0 lead 3:09 into the game after stealing the puck from defenseman Nick Holden in the neutral zone.
Zach Parise scored unassisted to make it 2-0 at 4:34 when he got his stick on a pass by forward Rick Nash from the bottom of the left face-off circle and the puck got past Lundqvist.
"That was the difference in the game, to be honest, capitalizing on some turnovers by them," said Parise, who has one goal and three assists during a four-game point streak. "They've got some important guys out of the lineup and hurt and some guys from Hartford [of the American Hockey League], so you want to make it tough on them. When we did that, we got rewarded; when we didn't do that, when we turned it over, we made it pretty easy for them."
Marcus Foligno scored with a one-timer from above the left hash marks off a pass from Daniel Winnik to make it 3-0 at 6:17.
Gilmour scored on the power play at 8:50 of the first to get the Rangers within 3-1. It was his third NHL game.