Last year's runner-up Andrey Rublev, however, missed out on a last-eight spot after falling to a three-set defeat against Jannik Sinner.
World No.3 Zverev overcame Spain's Pablo Carreno Busta 6-2 7-5 to progress in Monaco, where he is seeking to win the sixth ATP 1000 title of his career.
"For the second clay-court match of the season, I can't complain too much," the 24-year-old No.2 seed said on court after sealing the victory.
"Yes, I lost focus a little bit in the second set, but at the end of the day, he's somebody that can really play. I'm happy with a two-set win."
Tsitsipas, the No.3 seed, remains in contention for a second consecutive title in the principality after defeating Laslo Dere 7-5 7-6 (7-1) and will face off against No.12 seed Diego Schwartzman for a semi-final spot after the Argentine defeated Lorenzo Musetti in a hard-fought three-set encounter.
There will be no repeat of 2021's final between Tsitsipas and Rublev, however, after the Russian fell to a thrilling 5-7 6-1 6-3 loss to ninth seed Sinner in the day's final contest.
The other seed to fall victim to a shock in the last 16 was world No.7 Casper Ruud, losing 6-3 7-5 to Grigor Dimitrov, who will face Poland's Hubert Hurkacz in the last eight.
Finally, Novak Djokovic's conqueror Alejandro Davidovich Fokina cruised past David Goffin 6-4 6-1 to set up a quarter-final tie with the United States' Taylor Fritz, who bested compatriot Sebastian Korda – with whom he played doubles with in Monte Carlo – in straight sets.