There were questions about how prepared Zverev would be to face the energetic Alcaraz after playing the longest match of the tournament on Monday - a near five-hour, five-set marathon in punishing conditions against Jannik Sinner.
And while the 2020 U.S. Open finalist showed up ready to fight his tank emptied quickly, the 12th seed unable to keep pace with Alcaraz as the defending champion stepped on the gas to pull away for a straightforward win.
Alcaraz had only four break point chances throughout the entire contest but made each one of them count against a player starting to hit top gear again after an ankle injury last year.
"I remember the last time I played him in Madrid," Alcaraz said of the clash in May when Zverev lost tamely.
"I was sad about it because we've played big matches. Seeing him in the quarters of a Grand Slam again playing at his best, I'm so happy for him."
"He was struggling a lot, working really hard to come back at his best and finally we all see him showing his best tennis."
Medvedev reached the last four by beating eighth seed Andrey Rublev 6-4, 6-3, 6-4 in stifling heat but by the time Alcaraz and Zverev appeared on Arthur Ashe for the late match much of the sting had been taken out of the brutal conditions.
Zverev, with his booming serve finding the mark, was able to keep pace with Alcaraz through the early part of the first set.
Alcaraz capitalised on his one break chance of the opener to go up 5-3 and then quickly held serve to take control.
As Zverev's resistance dropped Alcaraz broke again early in second, delighting the crowd with some highlight reel shot-making and twirling his racquet like a baton.
"Of course, I'm playing to myself and to my team. But I try to make the people enjoy watching tennis," Alcaraz said.
"Trying to do different shots that probably the crowd are not used to seeing in matches, drop shots, going to the net. I always say 'put a smile'. I think people enjoy it as well."
Another break to get in front 5-2 and a hold left Alcaraz with a big smile and Zverev calling for a medical time out.
He returned for the third set with a heavily strapped groin and fought on bravely until Alcaraz grabbed another late break before serving out for the win.
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