The world number four needed just 66 minutes to secure a 6-4, 6-3 win and reach the semi-finals for the fourth time at the clay-court event.
His 43rd win of 2024 took him past the mark of world number one Jannik Sinner.
"I'm extremely pleased with the level of tennis today," said Zverev who showed no sign of the knee injury he suffered in his fourth round exit at Wimbledon.
"I'm happy to be in the semi-finals, but I don't want to stop here, I want to continue and hopefully defend my title here in Hamburg."
French Open runner-up Zverev is playing his last tournament before heading back to Roland Garros to defend his Olympic title.
That golden moment came at the delayed Tokyo Games of 2021, a year which saw him claim 59 tour-level wins and six titles.
"2021 was strange, because I started the season OK, I was playing well, but then the second half of the season, I barely lost a match," he added.
"So I hope if it goes like that this year, especially with the Olympics and especially with the US Open, I'll be the happiest person on the planet."
On Saturday, Zverev faces Spain's Pedro Martinez who knocked out Argentine fourth seed Francisco Cerundolo 1-6, 6-1, 6-4.
