The 26-year-old forward missed the first six games of the season with a broken left ring finger
The 26-year-old forward missed the first six games of the season with a broken left ring finger but Hayward, who led Utah last season with 19.7 points and 3.7 assists a game, made the most of his season debut in a Madison Square Garden matinee.
"First off, it felt great just to be out there," Hayward said. "You work all summer to be able to play, and so to have the injury was definitely unfortunate, but it's good to be out there with the guys.
"It's a little awkward playing with the splint for sure, but it's not going to stop me from getting out there on the court when it's time to play."
Rodney Hood scored 12 of his 18 points in the fourth quarter as the Jazz (4-3) outscored New York 36-29 in the last 12 minutes.
George Hill added 23 points and nine assists for Utah while Frenchman Rudy Gobert scored 13 points and grabbed eight rebounds and Derrick Favors scored 13 points and grabbed six rebounds.
"It gives us another guy who can demand double-teams and can create," Hill said of Hayward's return. "It just gives a whole other dimension."
Carmelo Anthony had 28 points and nine rebounds for the Knicks (2-4) while Kristaps Porzingis scored 28 points and grabbed eight rebounds for New York.