Oklahoma City's win also prevented the Spurs from clinching a playoff berth.
It was Krstic who hit the game-winning jumper with 51.6 seconds to play, giving Oklahoma City a 96-93 lead.
Tim Duncan cut the lead to one point with a tip-in with 36.9 seconds to play and then blocked a shot to give the Spurs a final try for the win. However, Michael Finley's jumper at the buzzer hit the rim.
Duncan was the leading scorer for the Spurs with 21 points and 12 rebounds. Finley added 14 and Manu Ginobili had 17.
The Spurs are tied with Houston for first place in the Southwest Division.