Hayward had been sidelined since breaking his right ring finger in training camp. He led the team in scoring last season, averaging nearly 20 points per game.
The Jazz reeled off nine straight points to begin the fourth quarter for an 87-80 and never trailed again.
Porzingis and Anthony combined for 24 points in the first quarter, shooting 10 of 12 to help the Knicks take a 30-20 lead.
Hayward scored 10 in the second quarter as the Jazz closed to 54-49 at halftime. Porzingis and Anthony totalled 14 points in the third period for an 80-78 lead.
Hood scored 12 points in the fourth quarter, as did Rose.
Knicks: Coach Jeff Hornacek praised Hayward before the game, saying, "If he wasn't in the West, he'd probably have been an All-Star by now." The coach added: "I think the game has slowed down for him. It seems very easy for him. He knows exactly what he's doing out there in pick-and-rolls, where to get his shots, when to take the big shots." . Maurice Ndour and Marshall Plumlee were inactive.
"People lead in different ways," Rose said. "You have your leaders like Kobe (Bryant). He's more personal, he's more intimate and in your face about it. You have leaders like myself and you've got Tim Duncan, where we lead by example by coming in every day, being consistent with our workouts and just showing people that we're focused and we're trying to get better. I lead by example."
Jazz: Visit Philadelphia on Monday.
Knicks: Host Brooklyn on Wednesday.