The defending champion hurt his left knee in a fall at Wimbledon but advanced 6-2, 6-2 past 114th-ranked Dutchman De Jong to set up a meeting with France's Hugo Gaston in the pre-Olympic clay-court tournament.
"I was still unsure this morning if I was going to play or not and during the warm-up I was in quite a lot of pain," said the German world number four.
"But somehow when I step on this court it disappears a little bit when the adrenaline gets going.
"I have an injury where I know where I stand and it will take time to heal. It won't heal in the next few days, it will take weeks and it's up to me if I am going to play like that or not."
Zverev, who reached the fourth round on grass at Wimbledon, claimed his 41st match win of the season.
Third seed Sebastian Baez and fourth-seeded Francisco Cerundolo, both from Argentina, reached the quarter-finals Wednesday along with Italy's Luciano Darderi and Spaniard Pedro Martinez.