Three years after ending Serena Williams' storied career under New York's bright lights, Tomljanovic threatened to pull off another major shock on Arthur Ashe Stadium after snatching the second set in a tiebreaker.
The three-time grand slam quarter-finalist had Gauff under immense pressure after breaking back for 5-5 in the deciding set, before the third-seeded 2023 champion responded.
With a lunging backhand-down-the-line winner, Gauff finally prevailed 6-4 6-7 (2-7) 7-5 after two hours and 57 minutes of drama.
"It was a tough match," Gauff said after booking a date with Donna Vekic.
"I had chances for it to be straight sets. Ajla was tough. I felt like she was getting so many balls back. I'm happy to get through to the next round."
Unlike Gauff, world No.2 Iga Swiatek enjoyed a trouble-free stroll to open her bid for another grand slam triumph, the Wimbledon champion needing just an hour to dispose of Emiliana Arango for the loss of only three games.
And in the process of blasting 25 winners past the outclassed Colombian in a 6-1 6-2 trouncing, Swiatek wasted no time in creating a new world record for starters at Flushing Meadows.
The Pole's victory was her 65th consecutive first-round win, breaking the previous Open era record set by Monica Seles.
Not that the 24-year-old dedicated 'Swiftie' seemed too fussed about her latest landmark as she seemed rather more keen to chat animatedly about the news that had just broken of her heroine, Taylor Swift, announcing her engagement to Travis Kelce.
"Obviously she had a lot of boyfriends, so we know all about that. So hopefully this one will stick forever. Travis seems like a great guy. She seems super happy, so I'm happy for her," said Swiatek.
"Well, I'm just happy for her, because she deserves the best."
Swift is a bit of fan of Swiatek too, apparently, having once sent her a handwritten note to congratulate her on her 2024 French Open win while the player attended an Eras Tour concert.
And she would recognise that, at the moment, Swiatek might just be playing some of her very best tennis again.
She won 23 of the 26 points when she landed her first serve at Arthur Ashe Stadium, looking every inch the woman to beat after her recent rejuvenation which saw her lift her first Wimbledon crown in July before winning for the first time in Cincinnati.
"It was a solid match and I'm happy that I wasn't trying to overpower, but I was just solid," Swiatek said.
A second title for the 2022 champion would make Swiatek the first woman to win Wimbledon and the US Open in the same year since Williams in 2012.
The 24-year-old will also have a chance to go back to world No.1 should she win the title and Aryna Sabalenka gets knocked out before the quarter-finals.
In the next round, Swiatek will face world No.66 Dutchwoman Suzan Lamens, who beat 18-year-old US wildcard Valerie Glozman 6-4 6-2.
British star Katie Boulter, fiancee of Australian No.1 Alex de Minaur, bowed out to 27th seed Marta Kostyuk 6-4 6-4 in a first-round loss which will result in her dropping out of the world's top 50.
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