The No.1-seeded Wozniacki had to deal with Julia Goerges, who had won three of the pair's last four meetings, two of those wins coming in 2011 when Wozniacki was ranked No.1 in the world. And Goerges was serving bombs - she blasted seven aces during the match without a single double fault.
But Wozniacki was just too solid on the return, dropping serve twice but more than making up for that with four breaks of her own, and the Dane eventually saw Goerges off in straight sets, 6-4, 6-4.
"Maybe it wasn't the most comfortable match out there, but she's always given me a lot of trouble in the past, so I knew this wasn't going to be an easy one," Wozniacki said in her post-match presser. "I just kept fighting. I tried to be more consistent than her, and I think I managed to do that. Sometimes you need to know your strengths and your weaknesses. And I think I served well today as well.
"She's got some big shots, so I'm just happy to be through to my first semifinals here."
Awaiting Wozniacki in the semifinals is No.4 seed Barbora Zahlavova Strycova, who dug out of a 5-2 hole in the second set to close No.7 seed CoCo Vandeweghe out in straight sets, 6-4, 7-5. The Czech dropped just three points during that five game run to close it out, winning 20 of those 23 points.
Wozniacki leads Zahlavova Strycova in their head-to-head series, 3-1, but Zahlavova Strycova's one win did come in their last meeting, a 6-2, 7-5 win in the fourth round of Wimbledon last summer.
"Barbora's a very different player," Wozniacki said. "Maybe she doesn't have the most power, but she places the balls really well, she has good hands and good volley skills, and she's definitely improved her game a lot in the last year. With age and experience she's really matured as a player."
Williams faced a nemesis too - Elena Vesnina had won two of their three previous meetings. But this time Williams was just too strong, the No.3-seeded American rallying from 4-2 down in the second set to move through in straight sets, 6-2, 6-4, and even up the pair's head-to-head series to 2-all.
"Things seemed to be going on serve, but then she had a big game for a break and another big game for a hold, and things were getting really interesting," Williams said of the second set. "She was really picking up her level. But after that, I don't know, the games came and then it was over.
"That's what you have to expect every time. Nobody's going to give it to you."
Williams and Davis will play against each other for the first time in the semifinals.