Britain's Emma Raducanu said she needed a "monumental effort" to beat Colombia's Camila Osorio and reach the Washington Open quarter-finals.
Raducanu, who will start the defence of her US Open title this month, won 7-6 (7-5) 7-6 (7-4) in two hours 50 minutes.
"It just gives you a lot of confidence coming through a match like that," said the British number one.
Compatriot Dan Evans progressed as American Taylor Fritz retired.
In hot and humid conditions, second seed Raducanu and Osorio required medical timeouts.
"For me it was a pretty monumental effort to really get through that," said Raducanu.
"There were many moments in both sets where you want to go for the easy option of trying to finish the point early, but I'm just really pleased and proud of how I dug in when it really mattered."
Raducanu will play Russia's Liudmila Samsonova in the last eight.
British number two and 16th seed Evans, who saved match point but was leading 3-6 7-6 (8-6) 4-1 when Fritz withdrew, faces Yoshihito Nishioka of Japan in the quarter-finals.
Fritz said he felt "embarrassed" at not being able to finish the match, but that he had been wearing a protective boot since Wimbledon last month because of a foot injury.
"I constantly felt like I was going to pass out, my vision was going fuzzy," he tweeted.
"The only thing that can really prepare me for playing in these conditions... is playing in these conditions, something I just haven't been able to do while nursing my foot.
"Now that my foot feels better I can finally put in the on-court work and be prepared for the rest of the year. Sorry if I worried anyone."
British number one Cameron Norrie beat Moldova's Radu Albot 6-3 7-6 (7-4) to reach the semi-finals of the Los Cabos Open in Mexico.
Defending champion and third seed Norrie will play second seed Felix Auger-Aliassime in the last four, and has lost all four of his previous meetings with the Canadian.
"Every time I play Felix he plays really well and has beaten me every time, so I am going to have to play well," Norrie said.
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