Gauff has become a headline act at the tennis match, not only after becoming the youngest player to qualify for the tournament but also when she beat her idol, five-time Wimbledon champion Venus Williams.
Eighth seed Svitolina also advanced with a battling 6-3 6-7 (1-7) 6-2 victory over Greece's Maria Sakkari, needing six match points to win the contest. She then held on for the win after losing a service-break lead in the third set.
Gauff, the American teenager who has proved the revelation of Wimbledon's first week by reaching the fourth round of the women's singles, was still pinching herself at her celebrity status. In the second round, Gauff got to play against Magdalena Rybarikova where she was able to pull off a second straight win.
Earlier on Centre Court, Halep comfortably defeated fellow former world number No 1 Victoria Azarenka in a match where the Belarussian imploded.
Gauff is ranked 313th in the world and is taking part in her first Grand Slam.
After her aggressive style paid off there, it was Hercog who really went into a shell, playing so cautiously and making mistake after mistake. The pause didn't alter the momentum as Gauff led 4-1 in the third, only for Hercog to get to 4-4 despite leg cramps surfacing.
It's a quality that her strength and conditioning coach, Jeff Drock, said she's always had.
Hercog won the first set, marking the first time in the tournament that Gauff dropped a set.
"Then after the next day, after I played Venus, everybody was screaming my name".
"The most unexpected message I received wasn't really a message", she said.
Men, women, girls and boys scanned the horizon at the All England Club yesterday evening, looking for a scoreboard to make sense of the roar rising from Centre Court.
"I think I'm just going to approach her like every other match I have been approaching". Poor Hercog did nothing to deserve that (and they certainly did boo her), but the crowd was firmly behind the 15-year-old who, save for a few cheers and fist pumps when the game turned around, was calm and focused through the entire match. "Even when I was down match point they were still cheering me on". Gauff's parents own a sports bar in Delray Beach, Fla., and there was a watch party there on Friday.