LeBron James had 31 points in the losing effort as Cleveland falls to 1-3 on the year.
The Jazz out rebounded the Cavs 41-30 and had 26 assists to the Cavalier's 6.
Kyle Irving had 34 points for Cleveland but the point guard had no assists. Kevin Love added 14 for Cleveland.
Hayward and Derrick Favors each had 21 points to lead the Jazz while Favors added 10 boards.
LeBron had this to say about the Cavaliers early season troubles.
''Rome wasn't built in a day and we understand that,'' James said. ''You have to continue to work the process. You hate to lose as competitors, but we felt like tonight we improved. We improved and proved in the second half we're capable of playing some good basketball.''
Read the Yahoo Sports article by Matthew Coles of the AP here.
Cleveland travels to Denver to face the Nuggets on Friday while the Jazz will host the Dallas Mavericks on the same day.