In her previous match the American had saved two match points against Polona Hercog before mounting an improbably comeback.
Gauff, who endearingly described herself on Friday as both "goofy and weird", said she hoped she had served as an example to many who were dreaming of making it in tennis. The Spanish player said: "I just will tell her that enjoy, and just work hard off court every time that she's on-court or in the gym".
Gauff's match with Halep, the 2018 French Open victor, is one of numerous highlights on what is known as Manic Monday because all 16 remaining men's and women's players in the draw are in action.
Bidding to become the youngest Wimbledon quarterfinalist since fellow-15-year-old Jennifer Capriati in 1991, the Atlanta native was by no means overawed, keeping the crowd entertained with some crashing backhands and athletic recoveries, but there were also far too many simple errors that the American was never going to get away with at this stage of the tournament.
"Well, I'm going to do it online", she said. Balancing different commitments within the same tournament can take a lot out of players but Williams suggested playing regularly was a positive for her.
Two-time Wimbledon champion Petra Kvitova plays Britain's Johanna Konta in what will be her first appearance in the last 16 since 2014 when she won the second of her titles.
"I'm definitely going to take some online courses".
Following her momentous win over former champion Venus Williams, Gauff graciously thanked the champion for everything she has done for the sport. It's her 51st Grand Slam quarterfinal for the seven-time Wimbledon champion.
Barty began perfectly, winning the first game of the match this way: 112 mph ace, 102 mph ace, 110 mph ace, 108 mph ace. But Halep overpowered her younger counterpart down the stretch to mirror her first set score of 6-3. Riske advanced to the quarterfinals of a Grand Slam for the first time in her career and defeated a top 5 ranked opponent for only the third time.
"I was sticking to how I wanted to play", Barty said.
Gauff, perhaps feeling ill, was seen by the trainer and doctor early in the second set and took medication.
Having won three matches in qualifying, each without dropping a set, Gauff outplayed Williams in the first round. Martic called for medical treatment on her left leg after the first game of the second set and her movement appeared to be hampered the rest of the way.
Also, Barbora Strycova came from a set and break down to beat Elise Mertens 4-6, 7-5, 6-2.