The German needed only 72 minutes to defeat American Marcos Giron 6-2 7-5 on Wednesday. He will now face either Italy's Lorenzo Musetti or France's Gael Monfils.
"He served incredibly well in the second set, so I'm very happy that I managed it in two sets," Zverev said.
The Tokyo 2020 Olympic champion is still suffering the consequences of pneumonia, which forced him to miss the China Open in Beijing last month.
"I'm not completely fit. It takes months, but I'm feeling better and better," he said.
Meanwhile defending champion Novak Djokovic has withdrawn from next week's Paris Masters.
The former top-ranked player said in an Instagram post he is "sorry to everyone who was hoping to see me play there".
"I have a lot of great memories winning seven titles there and hope to be back with you next year," he added.
Djokovic, 37, played at the Six Kings Slam exhibition last week but no reason was given for his withdrawal.
He has won a record seven titles at the Paris indoor tournament. His decision not to play could jeopardise his chances to qualify for the year-end ATP Finals.
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