Wilson pushed it to 3-1 at 7:05. He received a pass from Trevor van Riemsdyk and skated between Rangers defensemen Adam Fox and Niko Mikkola before beat Shesterkin from in close.
After Oshie hit the post on the rush, Sonny Milano knocked in the loose puck to make it 4-1 at 12:52.
Kuznetsov extended the lead to 5-1 with a backhand on a breakaway at 18:19.
"I think when we're giving up too many chances defensively, (and) that kind of leads to not really getting in a groove offensively," Rangers captain Jacob Trouba said. "It all kind of mixes together, so once we start taking care of the puck better, just giving up too many opportunities, we'll get it back."
Kreider made it 5-2 with a deflecction of Fox's shot on a power play at 6:49 of the third period.
Kuznetsov scored on a breakaway at 13:22 to make it 6-2, and Kaapo Kakko scored at 19:32 for the 6-3 final.
"I just talked to my dad yesterday," Kuznetsov said. "He's here, so I was like, 'Usually I got like six, seven breakaways a year and I got zero this year.' So I felt I just talked about that stuff with him the day before, and today I got two breakaways, so it's a process."
NOTES: The Rangers traded forward Vitali Kravtsov to the Vancouver Canucks for forward William Lockwood and a seventh-round pick in the 2026 NHL Draft before the game. ... Kreider has 11 points (six goals, five assists) in his past 11 games. ... Gustafsson has 10 assists in his past nine games. … Kuemper is 8-1-0 in his career against the Rangers. ... New York defenseman Ryan Lindgren left the game with an upper-body injury in the first period after he was checked into the boards by Oshie. Gallant said Lindgren is day to day and he will know more about his condition Sunday.