Venus Williams beat top seed Angelique Kerber on Wednesday to advance to a Miami Open semi-final against Britain's Johanna Konta.
American 11th seed Williams, who is seeking her fourth Miami title, survived a long first set before she completed a 7-5 6-3 victory over Germany's Kerber on a calm evening in south Florida.
Konta, the 10th seed, had earlier recovered from the brink of defeat to edge third seed Simona Halep in a three-set encounter that lasted two hours, 30 minutes.
Halep was only two points from victory in the second set, but could not put away her opponent, who pounced on the Romanian's evident emotional fragility to prevail 3-6 7-6(7) 6-2.
Williams, 36, whose previous Miami titles came in 1998, 1999 and 2001, will meet Konta in the semi-final, while Czech second seek Karolina Pliskova faces Danish 12th seed Carolina Wozniacki.
Williams, playing in front of a crowd that included her popcorn-munching father Richard, took nearly an hour to take the first set from Kerber, but made quicker work of the second.
Halep, meanwhile, got down on herself after losing the second set tiebreak to Konta.
"It was a really tough match, very high level," Halep told the WTA. "I was so close to winning, I was two points away in the tiebreak, but she played very strong and deserved to win."
Despite the result, Halep took comfort from a solid tournament as she works her way back from a knee injury.
"I'm happy to be here after the break that I had. I'm just disappointed I lost a match I had in my hands. But my confidence is there, the game is there, I just need to play matches."
Her post-match comments were more positive than her negative remarks to coach Darren Cahill after the second set.
"This is my character," Halep grumbled to her coach. "Two double faults at the end of the tiebreak and I miss all the balls."
Cahill told a sullen Halep she was a better athlete than Konta, imploring her to make her opponent run in the third set.
"You can write yourself off but I'm not writing you off," Cahill said. "It's up to you. It comes from within ... be brave in the big moments."
But Halep was completely outplayed in the final set, and she said afterwards her exchange with Cahill was nothing out of the ordinary.
"It's just my personality to be hard on myself. I want to change that in the future. I can say that I'm better than before, and I'm working on it."