Kevin Durant scored 36 points, including 16 in a row in the fourth quarter, and host Oklahoma City evened the Western Conference finals at two games apiece.
Serge Ibaka added a career-high 26 points on 11-of-11 shooting and Kendrick Perkins had 15 points and nine rebounds as the Thunder improved to 7-0 at home in the postseason.
Game 5 will be played Monday night in San Antonio. Only 14 teams have come back from a 2-0 deficit to win a best-of-seven series.
Tim Duncan scored 21 points and rookie Kawhi Leonard added 17 to pace six players in double figures for the Spurs, who lost their second straight game following a 20-game winning streak.
Durant, the league's three-time scoring leader, personally fended off San Antonio during a scintillating stretch of nearly four minutes, scoring 16 consecutive points after the Spurs had pulled within four to give the Thunder a 102-93 lead with 1:31 to play.
Leonard buried his second straight 3-pointer to cut the deficit to 102-96, but James Harden answered with a 3-pointer to make it 105-96 with 64 seconds left.
The Thunder had built their biggest lead at 68-53 on Ibaka's jumper with 5 1/2 minutes left in the third, but the Spurs ripped off 10 straight points, including 3-pointers by Stephen Jackson and Manu Ginobili, to get within 75-71 entering the final 12 minutes.
Ibaka hit his first six shots and scored 12 of his 14 points in the second quarter to spark the Thunder to a 55-43 halftime lead. Perkins had 13 points - matching his playoff high - and eight rebounds in the first half alone.
GAME NOTEBOOK: Ibaka, Perkins and reserve C Nick Collison outscored Durant, Westbrook and Sixth Man of the Year James Harden by a two-to-one margin (33-16) in the first half. ... The Spurs hit 11 of 23 3-point attempts and shot 50 percent (41 of 82) for the contest, but the Thunder shot 56.4 percent (44 of 78) and held a 41-31 edge on the boards.