Russell Westbrook added 22 points and seven assists for Oklahoma City, which bounced back from an overtime loss to Memphis on Tuesday. The Thunder, winners in four of five contests, moved to 15-3 this season in games played immediately after a loss.
Tyreke Evans had 30 points and nine rebounds for the Kings, who dropped their fifth in a row. Four of those losses have come by five points or fewer. Sacramento is 7-14 this season in games decided that margin.
Durant hit a pull-up jumper for a 97-85 Thunder lead with 3 1/2 minutes left, but the Kings, guided by 10 fourth quarter points from Evans, rallied. His layup after a long pass from DeMarcus Cousins had the hosts within a two points with 12.3 seconds left.
Durant was then fouled in the backcourt. An 88.5 percent free throw shooter, Durant missed a pair with 5.8 seconds left. Samuel Dalembert secured the rebound for the Kings, who called timeout with five seconds left.
The last play was set up for Evans, but his three-point try from the top of the arc clanked off the front of the rim and then the back. Omri Casspi's tip- in try was also off the mark as time expired.
"As a team we let up a little bit on the defensive end," Durant said. "We're up 12 with three, four minutes to go and we let up. It's not a good sign. I think you can't take away what we did all night on the defensive end, closing the paint up, forcing them to take some tough shots. It was a good all around game for us."
Durant scored 12 points in the opening quarter, helping the Thunder to a 27-24 edge after 12 minutes, this despite the visitors once facing a 16-8 deficit. Eric Maynor's desperation three-pointer capped the period.
Westbrook was a perfect 4-of-4 from the field in the second, as Oklahoma City expanded its lead to 54-45 at the half.
Oklahoma City was in front by as many as 11 in the third, but Sacramento surged back with eight straight points, finished by Evans' two free throws with 5:24 left for a 60-57 margin. The visitors led 75-72 going to the fourth.
The teams will meet Tuesday in Oklahoma City...The Kings finished 1-5 on their homestand and will embark on a seven-game road trip, beginning in Phoenix on Sunday...Last season, Sacramento posted a 13-9 mark in games decided by five points or less...Cousins had 14 points and 12 rebounds, while Casspi also scored 14 to go with nine boards...Durant, who had posted a double-double in each of his previous five games, had six rebounds...The teams were a combined 3-of-25 from three-point range.