It was Utah's fifth straight win as the Jazz (6-3) improved to 5-0 at home.
The Jazz are off to their best start at home since beginning the 2008-09 season at 6-0.
The Cavs (4-5) fell to 1-3 on a seven-game road trip, and visit Phoenix, the L.A. Lakers and Charlotte next.
Antawn Jamison led Cleveland with 22 points, including 13 in the third quarter, as he tried to rally the Cavs.
Utah dominated inside, with 56 points in the paint.
Cleveland pulled within six points midway through the fourth quarter before Josh Howard converted a three-point play. Jefferson then added a pair of jumpers, and C.J. Miles hit a late 3 to seal the win.
Rookie Kyrie Irving added 20 points for the Cavs.
Irving's driving layup pulled Cleveland within 106-101 with 57 seconds remaining. But Miles, who had played only 13 minutes combined in the previous two games and was in a shooting slump, hit a 3-pointer with 36 seconds left to bump Utah's lead back to eight.
The Cavs trailed 85-80 entering the fourth, and were within 91-85 when Howard was fouled, got the goaltending call and made the free throw.
In the third, the Cavs opened on a 13-7 run, with Jamison scoring 13 in the period. But Jefferson scored 14, and each time Cleveland made a move, Jefferson countered.
Tristan Thompson's jumper pulled the Cavs within 94-87, but Jefferson hit a 7-footer. His 14-footer gave Utah a 100-89 lead.
Utah led by nine at halftime 52-43, thanks to 32 points in the paint and 61.5 percent shooting, including 8 of 8 for Millsap
Millsap started 9 of 9.
The Jazz outscored Cleveland 11-1 to finish the second quarter after trailing 42-41 with about 5 minutes left in the half. Millsap started the run with his seventh straight field goal, Jefferson followed with a jumper and Devin Harris hit a 3-pointer.
Cleveland shot just 39 percent in the first half, with Jamison making just 3 of 12.
The Jazz led 27-26 after the first quarter. They got 20 points in the paint and a 3-pointer by Earl Watson at the buzzer. There were 12 lead changes and four ties in the first quarter.
Irving had six points in the first six minutes, but didn't score again until his 3-pointer with 8:22 left in the third.
NOTES: The wife of Utah guard Raja Bell gave birth to the couple's third son at 11:18 a.m. Tuesday. The boy weighed in at 4 pounds, 12 ounces. The couple has yet to announce a name. Bell started 0 of 2 and finished six points. ... Jazz center Jefferson has dropped 8 pounds since the start of training camp as planned. ... Jazz coach Tyrone Corbin has yet to select a captain. ... Cavs guard Irving entered the game averaging 15 points — most among rookies.