Fearnley – who returns to the United States having undergone a rapid growth in the game while at college in Texas – claimed the 7-5 6-2 5-7 6-4 victory in three hours and 26 minutes, avoiding adding his name to a list of four fallen Brits on day three at Flushing Meadows.
The 24-year-old looks to close out something of a breakthrough 2025 campaign, which kicked off with a notable victory over Nick Kyrgios at the Australian Open, on a positive note.
He was sturdy in his early ventures against the 37-year-old Bautista Agut. He saved a set point in a momentary scare and went on to claim the first break of the match to avoid a tie-breaker.
The second set was altogether more convincing for the Brit as he remained rock-solid on serve, and gained a decisive double-break advantage to emphatically move within a set of victory.
But in the third, the serve with which he had looked so comfortable began to falter.
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That was even after he gained an immediate break advantage. His experienced counterpart responded with three breaks of his own, helped by a generous supply of double faults as Fearnley admitted to nerves at getting the match over the line.
“It’s definitely nerves,” he said. “Obviously you’re going to double fault, you’re never not going to double fault, but 18, that’s too much.
If you look at when the double faults are happening, it’s when I’m serving for the match, serving to stay in the set. It’s at the highest tension moments.
“It’s helpful to know that even hitting all those double faults I can still win the match. That’s a positive. There’s good days, there’s bad days. In recent big matches, the double faults have been a little bit of an issue.”
He added: “Even though I’ve had some pretty big match experience, it’s still all relatively new for me and being in these kind of moments and these matches, it still gives me a lot of nerves.
“Maybe more than it necessarily should. I’m sounding like I’m a nervous wreck, I’m not, I’m fine. Just sometimes in those big moments, I need to be a little bit more clear and that will come with experience. It’s not something I’m worried about.”
Bautista Agut had all the momentum, and when he gained an immediate break advantage in the fourth set, there was some plausible concern for the Brit – but he avoided a capitulation with an astute response, hitting immediate back-to-back breaks to once again take control of the tie.
This time, Fearnley saw it through, and did not even give as much away as a break point for the remainder.
“I’m pretty tired right now,” said Fearnley. “I don’t really know what to make of it. Obviously to get over the line is really good. I was playing great first two sets and then got a little bit nervous and Roberto makes you earn it. When you’re nervous, that’s going to have its effect.”
Zverev powers past Fearnley to end Brit’s run – Australian Open highlights
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In sealing the win, Fearnley avoided joining Sonay Kartal, Katie Boulter, Fran Jones and Billy Harris in suffering first-round exits on Tuesday.
Fearnley will face Zverev in the second round, after the German came through in straight sets against Alejandro Tabilo.
After a difficult Wimbledon first-round exit, Zverev laid bare his mental struggles, saying he felt “lonely” and lacked joy “in everything I do” – but appeared to have his on-court mojo back on Arthur Ashe Stadium with a dominant display.
The world No. 3 did not drop a single break in the two hours and nine minutes on court, as he progressed with a 6-2 7-6(4) 6-4 win.
Their second-round meeting offers Fearnley the opportunity to avenge the straight-set defeats he suffered to Zverev in the third round of the Australian Open in January and two months later in Miami.
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