Kyle Connor had a goal and two assists, and Mark Scheifele scored two goals for the Jets (35-21-1), who had lost two straight. Morrissey and Mason Appleton each had two assists.
Vincent Trocheck scored for the Rangers (33-15-9), who were 8-0-2 during their point streak. Igor Shesterkin made 17 saves.
"[Hellebuyck] was great, not a lot of rebounds," Rangers captain Jacob Trouba said. "He was where he needed to be. Simple. He doesn't get out of position or make the acrobatic, crazy save because he doesn't put himself in that position. He was good, controlled the rebounds and there wasn't a lot of second chances for us."
Pierre-Luc Dubois gave the Jets a 1-0 lead at 5:12 of the first period on the power play when he tipped in Morrissey's shot from the high slot. Morrissey has 58 points (11 goals, 47 assists) in 57 games this season, passing Dustin Byfuglien (56 points in 78 games in 2013-14) for the most in a season by a defenseman in Jets/Atlanta Thrashers history.
"[The record] means a lot," Morrissey said. "I'm more worried about how we're doing as a team and how we're playing. But when you remove that and look at it, especially considering the relationship I had with 'Buff' and him being my first partner when I came into the League, I credit a lot of the confidence I had early in my career to playing with him and his attitude. It definitely means a lot to me, and it's a function of opportunity and us having a great team and great players that make my job easy. Just have to get them the puck and good things happen."
Scheifele made it 2-0 at 16:32, knocking in a rebound at the right post shortly after a Rangers' power play expired.
"We had to crank up our intensity," Bowness said. "We had to start working a lot harder tonight. The guys responded."
Connor extended it to 3-0 at 6:04 of the second period with a quick shot from the left hash marks.
"You're not going to keep them to nothing," Trouba said. "They've got some good players on their team, they capitalized on their chances, and we just didn't put ours in. Just one of those games."