NBA MVP Kevin Durant scored 25 points on 8-19 shooting.
It was a must-win matchup for the Thunder, who went into game three down 2-0 in the best--of-seven series.
The Thunder, who were heavily beaten in both the first two games of the series, were also boosted by the return of Serge Ibaka, who made a dramatic comeback from what was thought to be a season-ending calf injury. After collecting 15 points, seven rebounds and four blocks, Ibaka pointed to the sky as he left the game to cheers with 3:17 remaining and the Thunder ahead by 20 points.
"Obviously Serge came in and gave us a big lift not only on the defensive end but the offensive end," Thunder coach Scott Brooks said.
Thunder point guard Russell Westbrook led all scorers with 26 points while veteran Manu Ginobili had 23 for the Spurs.
The Thunder outrebounded the Spurs 52-36 after losing the battle of the boards in the first two games.
"I was very disappointed that we didn't come out with more of a foot in the neck sort of attitude," Spurs coach Gregg Popovich said. "They killed us on the boards, they beat us in 50-50 balls and that's very disappointing to me."
San Antonio won the first two games by a combined 52 points, but things were different from the start with Ibaka's return. Brooks also inserted speedy Reggie Jackson into the starting lineup in Thabo Sefolosha's place. Jackson finished with 15 points.
The crowd roared when Ibaka's name was announced during pregame introductions, and it got even louder when he started playing. He had eight points, three rebounds and two blocks in just over six minutes of play in the first quarter.
Twice in the final minute of the first half, Ginobili hit 3-pointers, and both times, Westbrook answered with a 3-pointer. The last one, with 0.6 seconds left, gave the Thunder a 57-53 lead. Oklahoma City shot 56 percent in the first half, but turned the ball over 12 times. Ginobili had 20 points and made 5 of 7 3-pointers before the break to keep the Spurs close.
Oklahoma City extended its lead to 83-76 at the end of the third quarter. A runner by Durant, then a 3-pointer by Caron Butler pushed the Thunder lead to 90-76 with just over 10 minutes to play.
Game 4 is in Oklahoma on Wednesday before both teams head back to San Antonio for Game 5. The winner of the best-of-seven series advances to the NBA finals against either Miami or Indiana.
- Additional reporting AP