The 14th-seeded American finally made it count after four hours and 45 minutes to pull through 7-6 (8/6), 6-3, 5-7, 5-7, 7-5 in New York.
Paul could have had a comparatively early night with two match points in the third set, but he failed to take them and a newly energised Borges of Portugal threatened to make him pay.
With the time in the “city that never sleeps” ticking past 1am and the Arthur Ashe Stadium mostly empty, the gruelling encounter went to a deciding fifth set.
Paul finally sealed the deal with a thrilling rally on his third match point, the exhausted pair exchanging a warm embrace at the net after an attritional battle. He will play the 23rd-seeded Alexander Bublik of Kazakhstan next.
In earlier men’s matches, Alexander Zverev’s Grand Slam experience proved decisive as the German third seed defeated Briton Jacob Fearnley 6-4 6-4 6-4, joining other seeded players Australian No 8 Alex de Minaur, Italian No 10 Lorenzo Musetti, Kazakh No 23 Alexander Bublik, Italian No 24 Flavio Cobolli and Canadian No 25 Felix Auger-Aliassime.
Stefanos Tsitsipas was knocked out by Germany’s Daniel Altmaier in the final match of the day on the Grandstand, with the Greek 26th seed falling 7-6(5) 1-6 4-6 6-3 7-5 in a marathon that lasted well over four hours.
On the women’s side, Coco Gauff said she felt more human allowing herself a moment of vulnerability under the primetime glare of Arthur Ashe Stadium, her tears and trembles visible to a crowd of 24,000 and millions watching at home, before reaching the third round.
After a three-set first-round victory that Gauff described as a mental battle, the 2023 champion once again faced a tough test against Donna Vekic before claiming a 7-6(5) 6-2 second-round win.
A flurry of errors and persistent serving struggles left the third seed on the brink of dropping the opening set, as she wept into her towel after surrendering her serve in the ninth game.
The 21-year-old later spoke about the moment, describing it not as embarrassment but as a reminder of her humanity under the sport’s brightest spotlight.
“It feels human. Being an athlete, people kind of disregard that side of us, the human side of things,” she said. “People say so many things, you know, you are number three in the world, and you’re doing this or you’re playing like this, and you should be better and things like that.
Next up for Gauff is No 28 seed Magdalena Frech of Poland, who rallied to beat Peyton Stearns 6-7 (6), 6-3, 6-2.
No 2 seed Iga Swiatek of Poland overcame a surprise second-set challenge from Suzan Lamens of the Netherlands and held on for a 6-1, 4-6, 6-4 victory. Swiatek next plays Russian 29th seed Anna Kalinskaya, who defeated Kazakhstan’s Yulia Putintseva 6-1, 7-5. (Agencies)