The 2024 runner-up kept alive her bid for a maiden major title, overcoming a resurgent Cirstea who had enjoyed a late-career renaissance, reaching a career-high top-20 ranking, before retiring at the end of the season.
There was little between the two on serve in a scrappy opening set, with only three holds between them. Pegula repeatedly handed Cirstea openings, including when she double-faulted while serving for the set, and then squandered four set points before finally converting the fifth as the 16th seed dropped serve again.
Pegula, who had needed three sets to overcome fellow U.S. Open finalist Leylah Fernandez in the previous round, gained the upper hand in a second set that followed a similar pattern, with the American securing one more break than Cirstea to create the difference.
The victory was Pegula's second over Cirstea in three weeks after she edged the Romanian in the Cincinnati Open Round of 16.
"I have a lot of respect for her. She's such a great competitor," Pegula said on the Louis Armstrong court.
"We actually hadn't played in a while up until the last few weeks. They were two really tough matches. It was definitely really intense."
Pegula will face the winner of the late-night clash between compatriot Emma Navarro and Russia's Anna Kalinskaya for a place in her third straight U.S. Open semi-final.