Rafael Nadal extended his unbeaten run over Frenchman Richard Gasquet to 15 to reach the Cincinnati Open third round.
The Spaniard, 31, who has not lost a set to Gasquet since 2008, won 6-3 6-4.
Roger Federer’s withdrawal from the tournament means on Monday Nadal will return to world number one for the first time since July 2014, taking over from Andy Murray who is also injured.
Meanwhile, Alexander Zverev’s 10-match winning streak ended with defeat by unseeded American Francis Tiafoe.
Zverev, 20, has moved up to seventh in the world rankings following victory over Roger Federer in Montreal.
But he lost 6-4 3-6 4-6 to 19-year-old Tiafoe, the world number 87.
Zverev arrived in Cincinnati having won back-to-back titles in Washington and Montreal, and he will start among the favourites when the US Open gets under way on 28 August.
“I’m not a machine. I’m tired. There was no hiding it. There’s a physical limit to all of us and I’ve reached that now,” Zverev admitted.
“This match is already forgotten. But it’s something that’s normal. It happens to all of us.”
Nadal, who won a record 10th French Open in June, will next face fellow Spaniard Albert Ramos-Vinolas.
“I work every day to play better. It’s obvious that was an important start for me, a good one.”
In the women’s event, world number nine Venus Williams was knocked out in the second round by Australian qualifier Ashleigh Barty.
Barty, ranked 48 in the world, beat the Wimbledon finalist 6-3 2-6 6-2 to earn her first victory over a top-10 player.
Williams, 37, served up six double faults in an error-strewn performance.
Barty, 21, will play world number five Caroline Wozniacki in the third round.
“It’s an honour to walk out on the the same court as Venus, to play against her and share the court with her,” Barty said.
“She’s a genuine champion of the game and has, I think, paved the way for us young players coming through so to play like I did, I’m really excited.”
Dane Wozniacki, one of four women who could replace Karolina Pliskova as world number one if results go her way this week, beat Russia’s Elena Vesnina 6-2 6-4 to progress.
But German Angelique Kerber, who could have moved up from third to first in the rankings, was beaten in a third-set tie-break by Russian Ekaterina Makarova, who converted her eighth match point to win 6-4 1-6 7-6 (13-11).
Simona Halep and Elina Svitolina, the final two women in contention for the number one spot, are yet to play their second round matches.
Elsewhere, American Madison Keys saw off Russia’s Daria Kasatkina 6-2 6-1, to set up a match against Wimbledon champion and fourth seed Garbine Muguruza of Spain.
Del Potro form continues
In the men’s event, Bulgarian Grigor Dimitrov recorded his 30th match win of the year to knock out Spain’s Feliciano Lopez 7-6 (7-5) 6-4 and will next face Juan Martin del Potro of Argentina.
Del Potro, who on Tuesday upset 10th seed Czech Tomas Berdych, defeated American qualifier Mitchell Krueger 6-4 6-4 in a hard-fought encounter.
The world number 30 saved five break points at 3-3 in second set and clinched victory on his fourth match point.
Australian Nick Kyrgios saw off Ukraine’s Alexandr Dolgopolov 6-3 7-6 (8-6) to advance to the third round, where he will face unseeded Croatian Ivo Karlovic.