New British men’s number one Draper, 22, earned a 7-6 (7-3) 6-3 victory over defending champion Alcaraz in the second round.
Spain’s Alcaraz, 21, saved three match points at 5-2 before Draper served out from 0-30 to the delight of an ecstatic home crowd.
It continued a memorable week for Draper after he claimed the first ATP title of his career at the Stuttgart Open on Sunday.
On Monday, he was confirmed as his nation’s leading player on the men’s tour.
“There was such a bee in my bonnet about winning an ATP event,” said Draper, who lost finals in Sofia and Adelaide before triumphing in Stuttgart.
“To get the title last week set me free of negative emotions and a lot of the pressure I’ve been putting on myself.”
Beating world number two Alcaraz – who claimed the French Open earlier this month – is the biggest win of Draper’s career by ranking.
He also ended three-time Grand Slam champion Alcaraz’s streak of 13 straight wins on grass.
Draper, who extended his winning run to seven matches, will play American fifth seed Tommy Paul in the quarter-finals on Friday.
Jack Draper has climbed to a career-high ranking of 31st in the world.
This match-up was a tantalising prospect which instantly caught the eye when the draw was made at the weekend.
The Wimbledon champion versus Britain’s most promising hope.