Also on Monday, Great Britain’s Cameron Norrie lost his third-round match to sixth seed Stefanos Tsitsipas.
Norrie improved in the second set when he recovered from being broken early but the Greek won 6-2 7-6 (7-1) to progress to the last 16.
“My patience and determination in the tie-break, trying to hang in there and make as many balls as I could and make as many balls as deep as possible so I didn’t have to defend much, was something that gave me the 7-1 in the tie-break,” said Tsitsipas.
“That was a relief. It was getting really close and the match was played in a few small details.”
World number one Iga Swiatek saw off a spirited effort from Germany’s Angelique Kerber as she triumphed 7-5 6-3 to set up a meeting with Keys in the women’s tournament.
The Polish top seed, who won the tournament in 2021 and 2022, squandered seven set points against Kerber before she finally closed out the first set.
Kerber won the first two games in the second set before Swiatek roared back to seal the match in one hour 38 minutes.
“Playing against Madison is not easy,” Swiatek said of her opponent in the last eight.
“The most important thing is to stay focused and really disciplined. That’s what I’m going to do for the next days.”
Elsewhere, in the last 16 Naomi Osaka lost 6-2 6-3 to China’s Zheng Qinwen.
Zheng, the Australian Open runner-up in January, reeled off seven consecutive games from 2-1 down in the first set.
She completed victory in one hour 24 minutes against Japan’s Osaka, who was making her first appearance at the tournament since 2021.
Zheng will play Coco Gauff in the quarter-finals after the American third seed fought back from a set down to clinch a 5-7 6-4 6-1 win over Paula Badosa of Spain.