Durant caught fire in the final 12 minutes, connecting on 7-of-9 shots from the floor as the Thunder held off the Spurs and forged a 2-2 tie in the best-of-seven series.
Serge Ibaka also provided some late-game scoring, hitting all 11 of his field goal tries en route to 26 points and helping Oklahoma City turn back a late San Antonio surge.
The Thunder improved to 7-0 at home in the post-season despite getting only two field goals from Russell Westbrook.
Tim Duncan had 21 points and eight rebounds for the Spurs, who will try to retake the advantage when the series moves back to San Antonio for Monday's Game 5.
Celebrity Families of 2014 [PHOTOS]