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Tsitsipas was too good for big-serving American John Isner in a 6-3 6-2 victory in Acapulco midweek.
A two-time Australian Open finalist, having also reached the French Open final four last year, Tsitsipas excelled on serve against Isner.
Greek star Tsitsipas only dropped one point on his first serve – not facing a break point throughout the last-16 contest – while firing down eight aces.
Standing in the way of Tsitsipas and a semi-final spot at the ATP 500 tournament is Canadian sensation Felix Auger-Aliassime.
In a battle of the NextGen, seventh seed Auger-Aliassime saved four of five break points in a 6-3 6-4 win over wild card Sebastian Korda.
Zverev will feature in his third Mexican Open quarter-final in four years after the second seed took down Laslo Djere 6-4 6-3.
Runner-up in 2019, Zverev will next face eighth seed Casper Ruud – who topped Tallon Griekspoor 4-6 6-3 7-6 (7-3) in the quarters.
"I think today what showed the most is that I got better with the match," Zverev said. "I started off extremely sloppy, started off with a lot of unforced errors.
"The longer the match went on the better I started playing and this is something that is very important for me. When I get into a rhythm I feel very comfortable on court and that's how I felt today."
Elsewhere, Lorenzo Musetti's giant-slaying run continued following a 2-6 6-3 7-6 (7-1) victory against Frances Tiafoe.
Musetti earned his first ATP 500 quarter-final as the Italian prepares to meet fifth seed Grigor Dimitrov, who eased past Miomir Kecmanovic 6-4 6-2.
There was an upset after fourth seed Raonic crashed out 6-4 6-2 at the hands of Dominik Koepfer, while sixth seed Fabio Fognini lost 6-4 6-3 against Cameron Norrie.