Andy Murray won his first singles match since pulling out of the individual event at the Olympics as he beat France's Richard Gasquet in Cincinnati.
Murray, a two-time winner of the Cincinnati Masters, won 6-4 6-4 and faces ninth seed Hubert Hurkacz or Alejandro Davidovich Fokina next.
But British men's number one Dan Evans lost 6-2 4-6 6-3 to Diego Schwartzman.
In the women's draw, Heather Watson progressed with a 6-2 3-6 6-1 victory over Belarusian Aliaksandra Sasnovich.
Murray, a three-time Grand Slam champion and winner of this event in 2008 and 2011, pulled out of the Olympic singles in Tokyo with a minor thigh strain.
The 34-year-old has been added to the US Open main draw - where he won his first Grand Slam title in 2012 - which begins on 30 August.
Both Watson and Evans had their first-round matches suspended because of rain on Monday.
Watson, who was 3-2 down in the second set, returned to seal a victory which sets up a second round meeting with Australian world number one Ashleigh Barty.
But world number 28 Evans, who was forced to miss the Olympics after a positive Covid-19 test, fell to a fourth successive loss since his third round exit at Wimbledon.
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