Durant only shot 9-for-24 from the field, but nailed 22 of 24 free throws, including a pair with 6.8 seconds remaining in the win. Thabo Sefolosha and Reggie Jackson each added 14 points as the Thunder (1-0) won without injured star point guard Russell Westbrook.
Gordon Hayward had a chance to force overtime, but his 3-pointer with 0.9 seconds remaining bounced off the rim.
Sefolosha hit a 3-pointer at the buzzer before halftime, helping Oklahoma City go into the visiting locker room ahead 57-48 thanks to a seven-point run.
This new look Jazz, who no longer feature old standbys Al Jefferson and Paul Millsap, didn't let them escape without a fight.
The Jazz weren't finished.
Mike Harris, an NBA journeyman who survived the final cut in Utah this preseason, hit three free throws after being fouled beyond the arc by Durant. The 6-foot-6 reserve forward, getting minutes because of Utah's injury situation, cut the Thunder's lead to 87-85 with a dunk midway through the fourth.
In his Jazz debut, Harris scored 13 points with four rebounds before fouling out.
NOTES: Westbrook could return sooner than expected, according to a Yahoo Sports report. Despite having a second surgery on his right knee earlier this month, the point guard is ahead of schedule and might return within two weeks. ... Thunder center Hasheem Thabeet missed the season-opener after being suspended one game for headbutting New Orleans' Greg Stiemsma in the preaseason. ... Utah began the NBA season with just 10 available players. Rookie Trey Burke (finger), Marvin Williams (Achilles heel), Brandon Rush (knee), Jeremy Evans (rotator cuff) and Andris Biedrins are all sidelined with injuries. Burke, the 2013 NCAA player of the year, will be evaluated in early November after having surgery on his fractured right index finger two weeks ago.