Draper's second career win over Alcaraz will see him break into the top 10 of the ATP Rankings for the first time in his career, with his win laced with intrigue from start to finish.
This bizarre match started with a blaze of powerful hitting from Draper, as he blew Alcaraz off the court to win the first set in double quick time.
With Alcaraz spraying errors at an alarming rate, he appeared to be a little rattled as he faced some powerful hitting from Draper.
Yet the young Spaniard is not a four-time Grand Slam champion for nothing and he powered back into the match with a stunning second set that he claimed without dropping a game.
Draper appeared to be struggling with the heat in Indian Wells as his game fell apart in that second set, but the real drama was still to come.
With the scores tied at 1-1 in the deciding set, umpire Mohamed Lahyani inserted himself into the story as he declared Draper had got to a short ball before it bounced twice.
Draper instantly called for a video review and it was clear the Brit had got his racket under the ball, with Lahyani then declaring the point should be replayed.
To add to the drama, Draper then asked for another video review as he claimed the point should be his as Alcaraz failed to get the ball back into play.
The correct decision may have been to replay the point, but it was awarded to Draper and he went on to break the Alcaraz serve.
He backed that up with another break of the Alcaraz serve as errors started to flow once again from the Spaniard, with Draper finally getting over the line after he served for the match for the second time.
"I've watched a lot of Carlos here and I was expecting him to come out all guns blazing," said Draper.
"It was the opposite. There were a lot of errors. Then in the second set, I lost concentration, the energy was drained from my body and I don't know what happened.
"I went to the toilet at the end of the set, looked in the mirror and said: 'You are in the semi-finals of a Masters 1000 and a win to make the top 10 in the world against Carlos Alcaraz in a full stadium. I had to give everything I've got. Don't worry about nerves. I had to go for it. Now I have to lift myself for the final."
When asked about breaking into the top 10 he added: "It feels unbelievable. When they said it on the court, I got emotional. I've been through so much in recent years with injuries. This is such a tough sport, we give so much to it. It feels incredible."
The magnitude of Draper's win was highlighted by the reality that he ended Alcaraz's 16-match winning run at Indian Wells and if the hype around the young Brit wasn't already reaching fever pitch, it will go into overdrive now.