Durant, who also had seven rebounds and five assists, got plenty of help from Reggie Jackson, who scored 27 points, including several big fourth quarter shots, dished out eight assists and had two steals.
Serge Ibaka added 14 points, nine rebounds, five blocks and two steals.
The Spurs were led by Tony Parker, who went off for 37 points. Tim Duncan scored 14 points and grabbed 13 rebounds.
This was a fantastic basketball and was closely contested throughout the evening. In the fourth quarter, the Thunder kept threatening to put the game away, but Parker continued to answer by slashing towards the basket and getting himself layups and open jumpers.
The biggest sequence came later in the fourth quarter. After Parker made two free throws to cut the lead to four, Durant answered with a three-pointer. Duncan lost the ball and Ibaka got free for a dunk. After Parker hit a 15-footer, Durant made another three to extend the lead to 108-98. The Spurs got another jumper from Parker and a three from Manu Ginobili, but Reggie Jackson slashed in for layup to give the Thunder a 110-103 lead with just 18.8 seconds to go.
The Thunder are now 33-10 while the Spurs are 32-10.