Britain's Johanna Konta beat Kiki Bertens of the Netherlands to reach the third round at the Cincinnati Open.
World number seven Konta broke early on in the first to take the set 6-3 with a strong performance on her first serve.
Bertens, ranked 27th, broke Konta in the second set but the Briton found three breaks of her own to win 6-3 6-3.
Konta will play either Alize Cornet of France or Slovakian Dominika Cibulkova next, while Wimbledon champion Garbine Muguruza beat Beatriz Haddad Maia.
Spain's Muguruza saw off the Brazilian 6-2 6-0 and will face either Russia's Daria Kastatkina or American Madison Keys in round three.
World number two Simona Halep beat American qualifier Taylor Townsend 6-4 6-1.
Romanian Halep plays the winner of Anastasija Sevastova and Roberta Vinci in the third round before a possible meeting with Konta in the quarter-final.
Earlier in the day, Wimbledon 2017 finalist and world number nine Venus Williams beat fellow American Alison Riske 6-2 6-0 to ease into the second round.
But this year's French Open winner Jelena Ostapenko was beaten 6-4 6-4 by world number 85 Aleksandra Krunic of Serbia.
And world number 10 Agnieszka Radwanska also failed to progress beyond the first round after being knocked out by Germany's Julia Goerges 6-4 6-4.
Del Potro through to second round
In the men's event, Juan Martin del Potro fought back from a set down to beat Tomas Berdych and reach the second round.
The Argentine, ranked 30th in the world, beat the Czech 2-6 7-6 (7-1) 6-0 in one hour and 55 minutes.
He will face American world number 244 Mitchell Krueger in the next round.
In round two, Austrian third seed Dominic Thiem beat Italy's Fabio Fognini 7-6 (7-5) 6-4 to set up a meeting with France's Adrian Mannarino or USA's Sam Querrey.
John Isner is also through to round three after beating fellow American Tommy Paul 6-3 6-3 and will next play either compatriot Frances Tiafoe or Germany's Alexander Zverev, who beat Roger Federer to win the Rogers Cup in Montreal on Sunday.
Elsewhere, Nick Kyrgios of Australia beat Belgian ninth seed David Goffin 6-2 6-3 to set up a second-round tie against Ukrainian Alexandr Dolgopolov.
The winner of that tie will play Ivo Karlovic in round three after the Croatian beat France's Jo-Wilfried Tsonga 6-4 7-6 (11-9).
And world number 10 Milos Raonic has withdrawn from the tournament with an injury to his left wrist.
The Canadian joins fellow top-10 players Andy Murray, Roger Federer, Kei Nishikori and Marin Cilic in missing the event, while 2016 US Open winner Stan Wawrinka and 12-time Grand Slam champion Novak Djokovic are out for the rest of the season.
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