The Jazz had started the final period trailing by three points (76-79) but managed to level the scores with a six and a half minutes remaining.
From there Utah took control and, with 155 seconds to play, had actually moved nine points in front before Milwaukee closed the gap to just two ??? but by then it was too little, too late.
Hayward potted 24 points in all and made nine of 10 free throws during the final quarter.
Elsewhere, Chicago eased past San Antonio 104-81 with Derrick Rose top-scoring on 22 points.?? ?? ????
Jimmy Butler added 17 points for the Bulls who won for only the third time in the past nine games and made it 10 successes from 16 against teams from the Western Conference.
And in Los Angeles, the Clippers enjoyed the widest winning margin of the night by easing past Brooklyn 123-84.
The Clippers all but secured their victory during a dominant second quarter during which they outscored the Nets by 36 points to 14.
Blake Griffin collected 22 points by half-time against the visitors who somehow managed to edge the final quarter by two points.
Meanwhile, it was a close run thing in Portland who lost by a single point to Boston 90-89, as Evan Turner’s three-pointer during the final few seconds proved decisive.?? ?? ?? ?? ?? ??
Guard Avery Bradley scored 18 points, and forward Jared Sullinger had 17 points and nine rebounds for the visitors who snapped a three-game losing streak.
Match winner Turner said: “I was able to shoot it high enough so it felt good. I kind of prayed to make a big shot and it happened.”