Britain's Johanna Konta won a hard-hitting contest against Slovakian Dominika Cibulkova to reach the Cincinnati Open quarter-finals.
The seventh seed won 6-3 6-4 to reach the last eight for the first time, setting up a rematch of her Wimbledon quarter-final against Simona Halep.
Romanian second seed Halep beat Latvian 15th seed Anastasija Sevastova 6-4 6-3.
Rain halted several third round ties, with top seed Rafael Nadal yet to start his match against Albert Ramos-Vinolas.
The winner of that all Spanish contest will face either Ivo Karlovic or Nick Kyrgios in the last eight - the Croatian led 4-3 when that match was postponed - with the victors due to play twice on Friday.
Bulgarian seventh seed Grigor Dimitrov beat Argentine Juan Martin del Potro for the first time in six attempts, coming through 6-3 7-5 to set up a quarter-final against Japan's Yuichi Sugita.
In the other men's quarter-finals, Austrian third seed Dominic Thiem will face Spain's David Ferrer, while American John Isner takes on another compatriot Jared Donaldson.
Konta, 26, did well to win a match that was far tougher than the straight-set scoreline suggests and break new ground in Cincinnati.
Five double-faults and a first-serve percentage of just 54% meant the Briton had to work harder than usual in her service games, with Cibulkova teeing off aggressively on the return.
Konta took the first set with two breaks of serve to one and looked to have the match well under control when she broke at the start of the second set.
However, Cibulkova refused to submit and had three break points for a 4-2 lead as a gripping set unfolded.
Konta clung on and grabbed her chance with a deep return on break point at 4-4 before serving out for a fine win, finishing with 24 winners to Cibulkova's 10.
Wimbledon champion Garbine Muguruza saved three match points on her way to beating American Madison Keys for the first time in four meetings.
The Spanish fourth seed came through 6-4 3-6 7-6 (7-3) to set up a quarter-final against Russian eighth seed Svetlana Kuznetsova, who beat Spain's Carla Suarez Navarro 6-2 6-4.
"You never knew who was going to win until the last point," said Muguruza. "I had match points against me so it was really hard. I battled back and I'm glad things went my way."
Sixth seed Caroline Wozniacki saw off Australian qualifier Ashleigh Barty 6-4 6-2.
The Dane could next meet world number one Karolina Pliskova, who was leading Italian qualifier Camila Giorgi 3-0 when play was suspended.
Fifth seed Elina Svitolina, who could become world number one if she wins the title, has yet to start her third round tie against Germany's Julia Goerges and could then also face the winner of another delayed match between American Sloane Stephens and Russian Ekaterina Makarova on Friday.
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.
Maria Sharapova is set to play in her first Grand Slam since her 15-month drugs ban after being given a wildcard for the US Open main draw.
Former world number one Sharapova, 30, returned to action in April but was denied a wildcard for the French Open.
The Russian five-time major winner was eligible for a place in Wimbledon qualifying through her world ranking, but missed the event with an injury.
The US Open will take place at Flushing Meadows from 28 August to 10 September.
"Her suspension under the terms of the tennis anti-doping program was completed and therefore was not one of the factors weighed in our wildcard selection process," The United States Tennis Association (USTA), which oversees the US Open, told BBC Sport.
"Consistent with past practice, a wildcard was provided to a past US champion who needed the wildcard for entry into the main draw.
"Previous US Open champions who have received US Open main draw wildcards include Martina Hingis, Lleyton Hewitt, Kim Cljisters and Juan Martin del Potro.
"Additionally, Sharapova has volunteered to speak to young tennis players at the USTA National Campus about the importance of the tennis anti-doping program and the personal responsibility each player has to comply with the program's requirements."
Sharapova returned to playing without a ranking in April and rose to 211 in the world after receiving wildcards in Stuttgart, Madrid and Rome.
She hoped to receive a wildcard for the French Open, but was denied one for both the main draw and qualifying rounds.
The 2006 US Open champion then elected to try to reach the Wimbledon main draw through qualifying, however she pulled out of the tournament having failed to recover from the muscle injury she sustained at the Italian Open the previous month.
She is currently suffering from a left forearm injury which forced her to pull out of this week's Cincinnati Open. She withdrew from the Stanford Bank of the West Classic earlier this month after suffering the injury in her first-round match.
In June 2016, Sharapova was punished with a two-year doping ban for testing positive for heart disease drug meldonium at the 2016 Australian Open.
It was reduced to 15 months following her appeal to the Court of Arbitration for Sport.
Rafael Nadal will be the new world number one from next Monday after Roger Federer withdrew from the Cincinnati Masters with a back injury.
The Swiss 19-time Grand Slam winner was the only player who could have denied Spain's Nadal taking the top spot in the rankings from Andy Murray.
Federer was injured in Sunday's Rogers Cup final defeat by Alexander Zverev.
Briton Murray pulled out of Cincinnati last week as he continues to recover from a hip problem.
Reigning French Open champion Nadal returns to the top of the rankings for the first time since July 2014.
The 31-year-old went out of the Rogers Cup in the last 16 against wildcard Denis Shapovalov.
Federer went all the way to the final before losing to 20-year-old German Zverev in Montreal - the Swiss' first tournament since winning Wimbledon for the eighth time in July.
"I am very sorry to pull out," said the world number three. "Cincinnati has some of the best fans in the world and I am sorry I will miss them.
"Unfortunately, I tweaked my back in Montreal and I need to rest this week."
The Cincinnati Master leads up to the the US Open, the final Grand Slam of the year, which begins on 28 August.
Federer, 36, joins fellow top 10 players Murray, Kei Nishikori and Marin Cilic in withdrawing, while 2016 US Open winner Stan Wawrinka and 12-time Grand Slam champion Novak Djokovic will miss the rest of the season.
Rafael Nadal fell to a shock defeat by 18-year-old Canadian Denis Shapovalov at the Rogers Cup in Montreal.
Wildcard Shapovalov came from a set down to beat top seed Nadal 3-6 6-4 7-6 (6-4) and become the youngest player to reach a Masters 1000 quarter-final.
Nadal's loss means Andy Murray remains world number one, but only until next week's Cincinnati Masters, where Nadal or Roger Federer will replace him.
Federer also progressed to the last eight, with victory over David Ferrer.
The Swiss world number three, 36, came from a set behind to beat the Spaniard 4-6 6-4 6-2 and next faces Roberto Bautista Agut, also of Spain, who defeated Frenchman Gael Monfils 4-6 7-6 (7-5) 7-6 (6-2).
World number 143 Shapovalov, the 2016 Wimbledon junior champion, plays 29-year-old Frenchman Adrian Mannarino.
In the other quarter-finals, Germany's Alexander Zverev, who beat Australian Nick Kyrgios 6-4 6-3, will play South African Kevin Anderson,who saw off American Sam Querrey 6-4 6-1 in the last 16.
And Argentina's Diego Schwartzman will face Robin Haase of the Netherlands. Haase beat Bulgaria's Grigor Dimitrov 7-6 (6-3) 4-6 6-1, while Schwartzman defeated American Jared Donaldson 0-6 7-5 7-5.