Cori Gauff's fairytale run at Wimbledon has continued. Photo: Toby Melville/Reuters

LONDON  Teenaged prodigy Cori Gauff reached Wimbledon's fourth round on Friday, clawing her way back from a set and 5-2 down to beat Slovenia's Polona Hercog 3-6 7-6(7) 7-5.

The 15-year-old American, ranked 313th in the world, had earned a match on Centre Court after capturing the public's imagination with her giant-killing exploits, including ousting former champion Venus Williams in the first round.

Gauff, who also beat former semi-finalist Magdalena Rybarikova in the second round, had the roaring support of the crowd but found it hard at first to cope with 28-year-old Hercog's heavy groundstrokes and big serve.

She showed remarkable composure, however, to fight back against the 60th-ranked Slovenian, who failed to convert two match points in the second set.

Hercog needed treatment on her back after the second set and slumped to 4-1 in the third but she too fought back in the tense duel.

She dumped a shot into the net in the final game, however, and another went long under Gauff's pressure before the teenager leapt in the air to celebrate her victory.