Adam Fox, Tye Karte, Adam Edstrom and Noah Laba also scored for the Rangers.
Vincent Trocheck had a pair of assists.
Igor Shesterkin made 24 saves for New York, who moved to 27-30-8.
Isak Rosen, Kyle Connor and Gabriel Vilardi scored for the Jets.
Connor Hellebuyck turned aside 11 shots for Winnipeg, who dropped to 26-28-10.
The Rangers got on the board just over a minute into the first with a power play marker when Adam Fox beat Hellebuyck with a slap shot from the point through traffic.
The goal was his 5th of the season.
Isak Rosen tied the game 2:21 into the second when he tipped a Jacob Bryson shot from the blue line past Shesterkin to score his first goal as a Jet.
The goal was his 4th of the season.
Alexis Lafreniere restored the one-goal lead at 7:36 when he deflected a Will Borgen shot from the point past Hellebuyck to make it 2-1.
The goal was his 19th of the season.
Kyle Connor tied it late in the second when Mark Scheifele stepped over the blue line on his forehand and hit Connor with a crisp pass.
The Jet winger did the rest, catching Ranger defenceman Adam Fox off guard as he skated around him before beating Shesterkin with a high wrister at 17:49.
The goal was his 29th of the season.
Mark Scheifele nearly gave the Jets the lead 35 seconds into the third when he hit the goal post on a breakaway.
Tye Karte scored 30 seconds later to give New York the lead when he tipped a Matthew Robertson shot from the left point past Hellebuyck to make it 3-2.
Gabriel Vilardi tied it at 4:19 when he converted snapped up a rebound off an Adam Lowry shot before moving to his backhand before sliding it past Shesterkin.
The goal was his 25th of the season.
Gabe Perreault made it 4-3 at 6:57 Braden Schneider spotted the Ranger winger driving the net and hit his stick with a hard pass from the point which he tipped past Hellebuyck.
The goal was his 2nd of the season.
Adam Edstrom gave the Rangers a two-goal cushion at 11:08 when he took a Vincent Trocheck feed from the side boards, one timing it past Hellebuyck with a low shot to make it 5-3.
Jets Head Coach Scott Arniel elected to pull his goaltender with 2:17 remaining in regulation.
Noah Laba added an empty netter with 50 seconds left in the third period to seal the win for the Rangers.
SHOTS-NEW YORK 17 WINNIPEG 27
ATTENDANCE-13,763
NOTES-Jets defenceman Dylan DeMelo played in his 700th NHL game against the Rangers.
