Fearnley’s progress has been so rapid over the past 15 months, it can be easy to forget how inexperienced he remains at the highest level.
Little over a year ago, the former US college student was ranked outside of the world’s leading 500 players.
Since then he has soared up the rankings – cracking the top 50 in June – after a stunning introduction to the ATP Tour.
Fearnley has a habit of drawing high-profile names early in the Grand Slams and has already played on some of the iconic courts in the game.
But in recent months his form has been compromised by a nervous tension which is particularly damaging to his serve.
Asked how he can solve the issue, Fearnley said: “I’m not too sure. I guess it’s helpful to know that even hitting all those double faults I can win the match – that’s a positive more than anything.
“There are good days and bad days, but in recent matches the doubles faults have been an issue.
“I’ll be playing Zverev next on another big court – a high-stakes, high-tense environment and I think putting myself in those situations will help.”
With Fearnley and Bautista Agut not taking to the court until after 8pm local time, a long night looking inevitable when the British number three finally secured a 62-minute opener.
When Fearnley used greater variety in the second and third sets – to move the world number 47 around – it reaped rewards.
Fearnley closed in on a relatively sharpish straight-setter when he broke serve early in the third – only for more double faults to help 37-year-old Bautista Agut extend the contest.
But he reset admirably in the fourth set, landing more first serves and limiting the double faults, to get over the line.
Surviving the first round meant Fearnley has now completed a full set of victories at the four Grand Slam tournaments.
“It was an extremely tough match, I knew Roberto would make me go right to the end,” said Fearnley, who wrapped up victory about 11:15pm local time.
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