Eric Staal, Zach Parise and Marcus Foligno all scored in the first 6:17 for Minnesota, which ran its home point streak to a franchise-record 13 games (10-0-3).
John Gilmour scored his first NHL goal in his third game for New York, and Kevin Hayes added his 13th goal of the season. Henrik Lundqvist stopped 26 shots for the Rangers.
The Wild haven't lost at home since Dec. 16 against Edmonton and own the league's longest home point streak of the season. They've outscored opponents 46-23 during the run.
Minnesota went ahead 3-0 for the third straight game. The Wild lost in overtime to Arizona and followed with a shutout of Chicago.
New York pressured, outshooting Minnesota 19-8 in the second period when Hayes scored his goal to bring the Rangers within one.
New York had won two straight after declaring themselves as sellers at the trade deadline and giving ice time to a host of young players, particularly on the back end, because of injuries.
Minnesota took advantage of the youth on defense by smothering the Rangers early.
Staal scored his 25th goal of the season three minutes in after getting the puck near the Wild's own blue line and tipping it past defenders twice on his way to the net. Staal has a four-game point streak and five goals in the past six games.
Parise added his third of the season less than two minutes later when he was in on the forecheck and poked at the puck in Rick Nash's control, and the puck got by Lundqvist.
After Foligno made it 3-0, Gilmour scored his first goal with a big slap shot from the point to cap the scoring in the first.
NOTES: Minnesota D Nick Seeler made his NHL debut a day after being recalled from the American Hockey League. Seeler, raised in Eden Prairie, Minnesota, was a fifth-round draft choice by the Wild in 2011. He becomes the 25th native Minnesotan to play for the Wild and the 51st Minnesota-born player to play in the NHL this season. ... Seeler made it eight native Minnesotans in Tuesday's game. According to the Elias Sports Bureau, the eight Minnesota-born players to suit up matches the most for a game involving the Wild, a feat that first occurred on Dec. 9, 2014 against the New York Islanders. Seeler, Parise, Matt Cullen, Nate Prosser and backup goaltender Alex Stalock were the Minnesotans for the Wild. Brady Skjei, Neal Pionk and Vinni Lettieri were the Minnesotans for the Rangers. Minnesotans Ryan McDonagh (New York) and Mike Reilly (Wild) were scratched. ... Pionk recorded his first career point with an assist on Hayes' goal in the second. It was his third NHL game. ... Foligno played in his 400th career game.
Rangers: At the New York Islanders on Thursday night.
Wild: Host Washington on Thursday night.
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ST. PAUL, Minn. (AP) - Devan Dubnyk made 32 saves, and Minnesota's early three-goal lead held up in 3-2 win over the New York Rangers on Tuesday night.