Jeff Green added 27 points and nine rebounds for the Thunders (3-2), while James Harden had 18 points, Russell Westbrook 17 and Serge Ibaka 12.
Durant was 10 of 23 from the field, including 3 of 5 from behind the arc, and 6 of 8 from the free throw line. He had nine rebounds and three assists.
Most of Durant's much-needed output came in the second half after the Spurs scorched the Thunder with 22 transition points in the first two quarters.
"We just had a lack of energy," he said. "The second half everybody was helping each other out, playing harder. Tony Parker broke us down a little bit early on. Our defense wasn't as tight as it should have been, but in the second half we did a great job of closing it up."
Parker and Manu Ginobili had 17 points each for the Spurs (3-3), while DeJuan Blair and George Hill both added 12.
Tim Duncan played only 12 minutes and scored 10 points for the Spurs, who led 29-28 after the first quarter.
Parker scored eight of San Antonio's final 22 points in the first half as San Antonio took a 10-point lead.
Ginobili finished 5 of 7 from 3-point range, He hit a 3 at the first-half buzzer to give San Antonio its biggest lead of the game, 61-51.
"They were running, and we were getting a little winded for some reason," Oklahoma City coach Scott Brooks said. "They did a good job of executing that in the first half."
The Thunder regained their composure, taking advantage in the low post to outscore the Spurs 28-14 in the paint and outrebounded them 28-13 in the second half.
"Sometimes when you push the pace, you get more possessions in the game that will lead to more scoring, but defensively, we did not do a very good job tonight," San Antonio's Richard Jefferson said.
Cole Aldrich (left AC joint sprain), Nenad Krstic (right index finger surgery) and Thabo Sefolosha (sprained finger) all sat out for the Thunder.
Tiago Splitter has yet to make his debut as a Spur. The Brazilian center has been sidelined with a sprained right plantaris muscle since the beginning of training camp.