The third-seeded Spaniard was well on top in the afternoon match at Rod Laver Arena against the Briton, who exited the court for a long medical time-out between the sets.
“This is not the way that I want to get through to the next round. I’m just happy to play another quarter-final here in Australia,” Alcaraz said on court.
“But really sorry for Jack. He doesn’t deserve to get injured. He couldn’t prepare the start of the season well.”
It was the second time Draper retired injured against Alcaraz, having cut short their 2023 match at Indian Wells due to an abdominal strain.
Alcaraz will meet the winner of 10-times champion Novak Djokovic and Jiri Lehecka, who play in the evening session, as he bids for a first semi-final at Melbourne Park.
Draper, the 15th seed, came into the match after winning three five-setters in the opening rounds.
A hip problem had hampered his preparations for Melbourne Park, forcing him to cancel plans to train with Alcaraz in Southern Spain during the off-season and to pull out of the United Cup team event.
Yet he would still have hoped to give Alcaraz a proper match, having proved a handful for the Spaniard previously.
Draper upset Alcaraz on grass at Queen’s in the lead up to Wimbledon last year and took a set off him in their first meeting at Basel in 2022.
The 23-year-old Briton dropped serve in the sixth game on Sunday but broke back to 5-4, leaving a frustrated Alcaraz ranting at the chair umpire about towels and serve clocks.
But while Alcaraz was still in search of his best tennis, Draper gifted him two set points with a wild forehand error.
The Briton saved one with a rush to the net and a volley into the corner but was picked off on the second as a sprinting Alcaraz whipped a forehand passing shot down the line.
The Spaniard’s momentum was stalled briefly when Draper called for a trainer and exited the court for a long medical time-out.
When play resumed, however, Alcaraz roared through the second set in just 38 minutes.
A physio went to Draper’s chair, the Briton shook his head and then shook Alcaraz’s hand, triggering groans from the centre court crowd.
“I’m just happy with the level I’m playing on the court and feeling really comfortable here in Australia,” said Alcaraz.
“Physically I’m feeling great, you know, coming to the second week of the Grand Slam.”
Alcaraz left his best wishes for Draper written on a camera lens before exiting the court.
“You will be where you deserved. Get well soon Jack,” the message read.