Having spent nine hours and 26 minutes on court during five-set battles with Lorenzo Sonego and Quentin Halys, Zverev had little interest in another marathon on Arthur Ashe Stadium.
The German made the perfect start, breaking Tabilo twice and dropping just one point behind his first serve in the opening set as he moved ahead in 38 minutes.
He appeared set for another comfortable set when he opened a 4-2 lead in the second, but his level dipped and Tabilo capitalised. The Chilean won three consecutive games and then earned two set points on Zverev's serve at 5-4.
Zverev held firm under pressure, saving both opportunities before breaking back to move ahead 6-5. Tabilo immediately responded with a break of his own, but the German dominated the ensuing tie-break to take a two-set lead.
"I am definitely happy with the improvements," Zverev said. "I spent 10 hours on the court in two matches so I had to find my rhythm somehow, and I did."
Tabilo threatened again at the start of the third set, earning two break points, but Zverev dismissed both with winners. From there, the second seed regained control, winning the final four games to complete the victory in two hours and 26 minutes.
"I was not happy with the second set," he admitted. "I think especially the end of the second set I lost focus a little bit. But I think the first and third sets are a big improvement to the other days."
The result sends Zverev into the second week in New York for the sixth time and sets up a fourth-round meeting with Luciano Darderi.
The Italian advanced with a 6-4, 6-3, 6-3 win over Australian wildcard Dane Sweeny. Darderi, who most recently beat Zverev in Rome in May after saving four match points, will now have another opportunity to derail the German's Grand Slam campaign.