Yet Riske, who once described herself as "100 per cent paranoid" and in a state of fear brought about by her dad's line of work, set about ending Barty's 15-match winning streak without a hint of intimidation.
Riske is relishing her reward of a showdown with Williams, who she has partnered in Fed Cup doubles.
"I'm so excited. I'm so proud of myself for the way I handled today's match and all previous matches".
"I am not comparing myself with a year ago, that was the best because I won the French Open".
Barty, 23, began the match with four consecutive aces and took the first set decisively before Riske staged her comeback in the 1:38 match.
"From the first Wimbledon I played, I met Phil. I think when I'm doing that, my best tennis kind of comes from that". The home crowd will once again be rooting for Johanna Konta, the last British player in the tournament, who faces Barbora Strycova. She did that today. I'm just looking to come forward as much as I can.
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"She's the greatest athlete I think that's ever been on the women's side".
Barty had not dropped a set through the opening three rounds at Wimbledon, only losing an incredible 12 games in total.
Positioned in a section described by veteran New York Times tennis scribe Christopher Clarey as one of the "craziest, nastiest grand slam quarters in the open era", Barty is still yet to face a seeded player.
For Riske, it was her 30th Grand Slam tournament, but she's only gone as far as the fourth round at the 2013 U.S. Open.
In other women's matches Monday, No. 8 Elina Svitolina beat No. 24 Petra Martic 6-4, 6-2, and Zhang Shuai defeated Dayana Yastremska 6-4, 1-6, 6-2.
The American had her opponent on the back foot and eventually got her chance to break at 4-3 and took her opportunity with a fine forehand victor down the line.
The battle between the "Karolinas" and the "Czechs" went on till the final set.
"Well, the last time I faced a fellow American I lost, so I definitely want to do well this time", Williams said.