A 3-point attempt by Gordon Hayward misfired with three seconds to go, leaving the shorthanded Thunder with a season-opening victory.
Oklahoma City began the campaign without the services of guard Russell Westbrook, who has had two knee surgeries since the end of last season.
Durant went to the foul line 24 times, making 22 of the attempts. He was just 2-of-8 from 3-point range, however, and the Thunder shot only 23.5 percent from the field in the final quarter to allow the Jazz to rally from an 11-point deficit.
Thabo Sefolosha and Reggie Jackson both scored 14 for the Thunder.
Utah was led by Alec Burks with 24 points off the bench.