This time, though, Gauff could not come through, beaten by the older, more experienced Halep 6-3, 6-3.
Williams, a seven-time Wimbledon champion who missed about a year of play while she had a baby in 2017 but returned to the tennis tour in 2018, entered the tournament without having played since the third round of the French Open - skipping the grass-court warm-up tournaments.
"If somebody told me this three weeks ago, I probably wouldn't believe it", the 15-year-old said.
"I enjoyed a lot the crowd, the energy today, I felt it really well".
"It is a good challenge, she is a top player and I will try my best to win the match".
"I am not comparing myself with previous year, that was the best because I won the French Open".
"I am trying to try my best every time I step on court".
The unseeded Riske, 29, upset world No. 1 and pre-tournament favorite Ashleigh Barty 3-6, 6-2, 6-3, ending Barty's 15-match winning streak to reach her first Grand Slam quarterfinal. To get there in the first place, Gauff became the youngest player to ever qualify for Wimbledon.
Having looked so assured in the first week - and a decent bet to end almost four decades of Australian being without a women's singles champion - she lacked the answers when required as Riske fought back to win 3-6, 6-2, 6-2.
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BBC commentator Tracy Austin, who won the US Open aged 16, said: Her fairytale ends here at Wimledon but it will continue.
After beating Polona Hercog to set up a Round of 16 battle with Halep, Gauff got plenty of attention of social media, with everyone from Michelle Obama to Joel Embiid chiming in to congratulate the Floridian on a comeback that took almost three hours.
The Florida native has Tallahassee connections as her mother, Candi Gauff, was a Florida State track and field athlete for four years from 1988 to 1992.
Coco immediately changed her plans, caught a flight to South West London and ended up storming through her qualifying matches, before drawing Venus in the first round of the main draw.
"I'm only 15. Like, I've not almost gotten [to] develop my game". Clarke finally praised Gauff: "You look at the people she's obviously being compared to and the past champions that have won this that have said it".
Halep then motored ahead in the second set, only for Gauff to bring it back on serve.
The 16 remaining players in both the men's and women's singles draw take to the court on the same day as they attempt to reach the quarter-finals of this prestigious Grand Slam.
She improved to 14-1 on grass courts this season and reached the first major quarterfinal of her career in 30 appearances. And she saved another couple at 5-2 down to prolong match. The duo reversed 6-1, 6-4 to Sweden's Robert Lindstedt and Latvia's Jeļena Ostapenko.