Wednesday's washout meant two matches in a day for nearly everyone, and British number one Konta produced two standout results.
Her 6-7 (3) 6-4 6-1 victory over French Open runner-up Stephens in the second round was arguably the most impressive of her career on clay.
— WTA (@WTA) May 16, 2019
Konta lost the opening set having held a 4-0 lead but recovered impressively, showing the significant improvements she has made on the surface this season.
Her only previous victory over a top-10 player on clay came against Roberta Vinci at the same venue three years ago.
Konta has had by far her best season on clay, reaching the final in Rabat earlier this month and now progressing to the last eight of one of the WTA Tour's biggest events.
Williams did not have to play twice, having been given a walkover in the second round by her sister Serena, and it was clear from the start of Thursday's match that she, too, was experiencing physical issues.
The 38-year-old had her right knee strapped and for the first two games she could hardly move or serve.
She improved after that but never looked capable of making a match of it as long as Konta kept her head, which she did to win 6-2 6-4 in just an hour and 12 minutes.
Konta will celebrate her 28th birthday on Friday with a clash against either Czech teenager Marketa Vondrousova, who knocked out Simona Halep in round two, or Russian Daria Kasatkina.
She is already set to climb back into the top 40 and one more victory could be enough for a top-32 seeding at the French Open, which begins a week on Sunday.