The Russian defeated the American Maxime Cressy (32nd) 6-4, 7-6 (10/8).
He was realistic in the first set, removed by converting the only break point he got.
In the second set, he had a harder time disrupting the opposing engagement, with Cressy netting 14 aces in total.
It was in the decisive game, very disputed, that he ended up winning after his third match point and 1h44 of play.
Rublev is looking for a 4th title this year, after those won in Marseille, Dubai and Belgrade.
Such a performance would make him the most successful player this season along with Rafael Nadal and Carlos Alcaraz.
He was to face in the afternoon Washington time, for his second match of the day because of the delay the day before due to the rain, JJ Wolf (99th), for a place in the semi-finals.
Recipient of a wild card, the American dismissed the Dane Holger Rune (28th) 7-5, 4-6, 6-3.
Another latecomer reaching the quarter, Nick Kyrgios completed his duel quite easily against Reilly Opelka.
The Australian, who was leading 7-6 (7/1), 2-1 when the match was abandoned on Thursday night, closed the deal by winning the second set 6-2.
He too will play again in the afternoon to try to reach the last four, against the American Frances Tiafoe (27th) who got rid 4-6, 6-2, 6-3 of the Dutchman Botic van De Zandschulp ( 26th).
The other two quarters will oppose the Briton Daniel Evans (40th) to the Japanese Yoshihito Nishioka (96th) and the Swede Mikael Ymer (115th) to the American Sebastian Korda (54th), who defeated the Bulgarian Grigor Dimitrov.
#photo1
Among the women, the Estonian Kaia Kanepi (37th) is the first to reach the semi-finals, after her victory 6-7 (4/7), 6-4, 6-3 at the expense of the Russian Anna Kalinskaya (71st ).
Belarusian Victoria Azarenka (20th) advanced to the quarterfinals, beating Czech Tereza Martincova 7-6 (9/7), 6-2.
She will play again in the evening against the Chinese Xiyu Wang (95th).
In the last two quarters, the British Emma Raducanu (10th), surprise winner of the US Open last year, will face the Russian Liudmila Samsonova (60th), and the Australian Daria Saville (88th) will challenge the Canadian Rebecca Marino ( 111e), resulting from the qualifications.
© 2022 AFP