Hayward had 22 points and went back and forth with James during a decisive third quarter. James brought the Cavs back from a 15-point halftime deficit before Hayward drove the lead back to 14.
Hayward had 11 points while the Jazz used a 16-0 run midway through the quarter to lead 74-60. The Cavs had a 17-0 roll after halftime thanks an aggressive James and his 13 third-quarter points.
Trey Lyles had eight straight points, including a pair of 3-pointers, in the fourth quarter to help the Jazz hold on.
James finished with 29 points and Kyrie Irving added 20 for the Cavs.