Draper won the first set against Shelton with an equally commanding performance in service as the one he produced during his fourth round victory against Taylor Fritz.
He conceded only three points on service, and a break was enough to secure the first set.
However, the partisan crowd did not take too long to find her voice, with the huge shots of Shelton, helping her win the first three games in the second set.
A frustrated draper received a warning for a driving in the form of yesteryear after hitting a bullet in the stands of the third match, but he refocused to force the use of the service.
The match turned decisively in his favor when Shelton Double defeated to give Draper a chance to serve for a place in the semi-finals.
He went 0-30 below but destroyed the following four points to ensure the victory.
“I had the impression that the conditions might suited me a little more,” said Draper at BBC Sport.
“His service would rebound very high if he was alive, but I thought it was a challenge for both of us dealing with the wind and dead conditions.”
However, the Briton does not expect such an advantage against Alcaraz.
“I think these courts bring out the best in him,” added Draper.
“He can show all his skills and seek his forehand.
“I think the conditions really suit him – but again, he does well in most cases.”
