Mikael Granlund, Jason Zucker, Matt Dumba and Charlie Coyle also scored for the Wild (21-8-4), who chased Henrik Lundqvist with four goals on 13 shots.
Coyle added three assists, while Koivu and Zucker had three points apiece. Eric Staal (two assists) and Granlund both finished with two points.
Darcy Kuemper made 31 saves in his seventh start of the season. His most notable stop was a diving, sprawling, glove save on a loose puck in the blue paint 6 1/2 minutes into the third period.
While the Wild are surging, New York dropped to 23-12-1 with its second consecutive loss in regulation.
Chris Kreider scored twice for the Rangers, who also got goals from Ryan McDonagh and Derek Stepan.
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NEW YORK (AP) - Mikko Koivu, Nino Niederreiter and Marco Scandella scored in a 5-minute span early in the second period, and the Minnesota Wild beat the New York Rangers 7-4 on Friday night for their franchise-record 10th straight win.