After twice needing to rally from a service break down in the opening set, Williams had to pull out all stops to deny the 55th-ranked Riske, who was anything but overawed contesting her maiden grand slam quarter-final.
Seeded 11th this year after losing the 2018 final to Angelique Kerber, Williams needed 18 aces and six services breaks to finally finish off the 29-year-old underdog after two hours and one minute.
Desperate to match Margaret Court’s record 24 singles majors, the 37-year-old Williams will play either British 19th seed Johanna Konta or unseeded Czech Barbora Strycova on Thursday for a place in Saturday’s title decider.
Earlier, Romania’s former world No.1 Simona Halep booked her place in the semi-finals with a straight sets win over China’s Zhang Shuai.
Halep, the seventh seed, fought back from a service break down in the opening set to win 7-6 (7-4), 6-1 to advance to the last four for the first time in five years.
Just as she did in quelling the lively challenge of 15-year-old Coco Gauff on Monday, Halep initially struggled and looked in real danger when 4-1 down and facing more break points in the opening set. However, the Romanian dug in to see off the threat then played her usual percentage tennis as Zhang lost her way.
“I fought hard in the first set, even if I knew I was 4-1 and she was hitting hard, I knew she would hit with a lot of power. I knew I would have to play aggressively and I did it great,” she said.
“I have energy, I feel fresh and confident and I am perhaps playing my best tennis on grass.”
Zhang is ranked 50th and has reached the quarter-finals in only one Grand Slam event – the 2016 Australian Open.
However, she started superbly, serving and returning with depth, power and confidence to break in the second game and race to a 4-1 lead. That looked set to be 5-1 but Halep battled and chased to save four break points in the game and turn the match.
The 27-year-old Romanian, last year’s French Open champion, began to find her own rhythm, delivering the calculated low-risk groundstrokes that wore down American Gauff on Monday to hold, then broke back via a double fault.
Zhang’s double-handed backhand, so deadly in the opening games, began to pepper the tramlines as the inconsistency indicated by her poor Grand Slam record became evident.
She clung on enough to get to a tiebreak but was well beaten in it and an early break in the second set put Halep 3-1 up.
Zhang’s head then dropped and the errors flowed as Halep rattled through the remaining games at a canter.