Ben Bishop, named a finalist for the Vezina Trophy during the game, made 30 saves for the win.
Asdrúbal Cabrera accounted for five runs, driving in three and scoring twice.
San Antonio had 60 points in the pain, only two off its Game 3 total, but they had 11 fewer second-chance points and nine less Fastbreak points.
It was completely out of character for White, but the mild-mannered point guard has never been in this situation before.
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Minor was at 96 pitches after getting the final two outs in the eighth on two pitches.
DeMar DeRozan said the Spurs still felt good leaving Denver despite blowing those big leads and a big opportunity to take a 2-0 lead.
Russell Westbrook, who had his ninth career postseason triple-double in Oklahoma City's Game 1 loss, finished with 14 points, nine rebounds and 11 assists.