With the set at 1-1, and the game 15-15, the ball was judged by umpire Mohamed Lahyani to have bounced twice before Draper reached a drop shot.
It was clearly a wrong call from the official, but players now have the benefit of using video technology in Indian Wells to question decisions over double bounces.
After Draper instantly asked for a replay, his challenge was successful and allowed Lahyani to overturn the original decision.
He was given the point for a 15-30 lead and, with momentum back in his favour, secured a break which ultimately proved the difference.
A thankful Draper said the video reviews – which are not available at every ATP event – are “really good for tennis”, although Alcaraz insisted he was not “affected” by the incident.
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However, his level dipped after that point as his bid to win Indian Wells for the third year running was ended.
Left-hander Draper goes on to face Denmark’s Holger Rune in Sunday’s final at the Masters 1,000 event in California.
Rune, ranked 13th, reached the fourth Masters final of his career with a 7-5 6-4 victory over Russian fifth seed Daniil Medvedev.