The German, who won Roland Garros and finished Wimbledon runner-up this year, earned his 46th victory of the season as he fought off the Frenchman, a 2025 Cincinnati semi-finalist.
Zverev finished off the match with a sizzling backhand down the line.
"This was a step up from my first match," he said. "He was playing incredibly aggressively, hitting forehands all over the court.
"I'm happy to be through in straight sets. He made it difficult for you to play aggressive yourself."
Williams sisters lose in doubles
Sisters Serena and Venus Williams, with 14 Grand Slam titles and three Olympic gold medals as a pair, took to the doubles court together for the first time since the 2022 US Open but lost to American Payton Stearns and Marta Kostyuk of Ukraine 6-2, 1-6, 10-8.
The siblings each lost serve once in the first set, Kostyuk serving out the opener as her team won six of the last seven games.
The sisters answered by dominating the second set and rallied after falling behind 6-0 and 8-2 in the 10-point tie-breaker third set, but lost when Venus double-faulted.
Minaur outlasts Fery
Men's fifth seed Alex de Minaur battled through multiple rain interruptions to defeat Arthur Fery 7-5, 7-6 (7/3).
The Australian was up a set and 5-1 after a 30-minute stoppage, but Wimbledon semi-finalist Fery erupted, winning five games in a row before de Minaur stopped the rot with a hold.
De Minaur reached the fourth round despite 29 unforced errors over nearly two and a half hours.
"You never want to go into a rain delay leading 5-1," he said. "It was a tough day with all the interruptions.
"I can't remember a match that started and stopped so many times. I'm happy with how I found a way. But it was harder at the end than it should have been."
Jodar moves on with ease
Spanish teen Rafael Jodar dominated Alejandro Tabilo of Chile 6-2, 6-1, advancing with just one unforced error to a foe that beat him five months ago in Indian Wells.
Jodar got through in 74 minutes to his 36th win of the season and will next line up against Roland Garros finalist Flavio Cobolli.
The Italian came from a breakdown in the deciding set to defeat Alexander Blockx 7-5, 4-6, 7-5.
"A Masters 1000 is something I dreamed of as a kid," 12th-seeded Jodar said. "I'm grateful for the position I'm in now. But I'm still the same as when I used to watch the matches on TV."
Meanwhile, Argentine Thiago Tirante, who ousted Novak Djokovic in the second round, defeated Spain's Martin Landaluce 7-6 (7/5), 7-6 (7/4).
Rybakina advances
Two-time Grand Slam champion Elena Rybakina shook off two one-hour rain stoppages to beat Magdalena Frech 6-4, 7-6 (7/2).
"It was a crazy day, to be honest, coming out every time into clouds and humidity," Rybakina said. "I was on top of the ball in the tie-break but it was a difficult one.
"I had the opportunities on the three match points but when you are tired it's difficult to keep concentration."
The second-seeded Kazakh admitted she struggled to close out a match which dragged on for much of the afternoon.
The players were forced off court after nine games of the first set and again in the seventh game of the second.
Swiatek battles back against Sakkari
Former world number one and defending champion Swiatek was done hours before the poor weather, turning the tables after losing the first set to defeat Maria Sakkari 4-6, 6-1, 6-1.
The Polish seventh seed, who won the Toronto title last week, improved to 6-4 over her Greek opponent, heading to the changing rooms after dropping the first set and returning as if another player.
"It's hard to analyse this match," Swiatek said. "I was playing good in the first set but I lacked precision, I was playing too much to her.
"After that I wanted to push her and not give so many opportunities. I'm happy it started working in the second set I played a bit better.
"She made mistakes and the momentum changed a little bit."
Pegula continues to roll
Pegula, a 2024 finalist, dispatched US compatriot Emma Navarro 7-5, 6-2, ending with an ace.