The fifteen-year old American sensation, produced her gutsiest performance yet to come through 3-6 7-6(7) 7-5 after two hours and 47 minutes on Centre Court. She will meet seventh seed Simona Halep in the fourth round.
Gauff stunned five-time champion Venus Williams on the opening day to emerge as the star of the championships, before following it up with victory over 2017 semi-finalist Magdalena Rybarikova.
The match with Hercog looked to be one hurdle too far as her previously impeccable game unravelled in the first two sets, but she somehow broke back in the second and held her nerve in the tie-break.
Gauff is the youngest player to reach this stage since Jennifer Capriati’s run to the semi-finals in 1991, also at 15. She came through qualifying after being handed a wildcard, the start of a remarkable story that has seen her knock out one of her idols and reach the second round of a Grand Slam at the first attempt. Now there will be at least one more chapter