Ginobili's performance in the fourth quarter helped rally the Spurs from an 11-point deficit and ran their unbeaten streak to 19 games dating back to the regular season.
Kevin Durant pumped in 27 points, grabbed 10 rebounds and blocked three shots for the Thunder.
Russell Westbrook was held to 17 points on 7-of-21 shooting in Oklahoma City's loss.
The Thunder will attempt to bounce back in Thursday's Game 2 at San Antonio.
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