Heading into game three on the back of two disappointing defeats, the Thunder were boosted by the return of Serge Ibaka at the Chesapeake Energy Arena.
The Thunder struggled to pull away from San Antonio in a first half when they repeatedly turned the ball over, and Manu Ginobili ensured the visitors stayed in touch with five three-point efforts before the interval.
An improved display at both ends of the court in the final 24 minutes earned Oklahoma a 14-point advantage early in the final quarter.
Ibaka, who was expected to miss the remainder of the playoffs with a calf strain, made a number of key defensive plays to make it difficult for Tony Parker to make a difference around the basket.
Russell Westbrook scored 26 points, while MVP Kevin Durant contributed 25 points and 10 rebounds as Oklahoma's lead never looked in danger during the closing stages of the contest.
The Thunder will host San Antonio again on Tuesday with the opportunity to level the series at 2-2.