Karolina Pliskova and Garbine Muguruza re-established order among seeds on Wednesday as both reached the quarter-finals of the WTA Dubai Championships.
World number three Pliskova strolled to a 6-1, 6-2 defeat of qualifier Kristina Mladenovic in barely an hour, before ninth seed Muguruza took almost two-and-a-half hours to get past Russian Veronika Kudermetova 7-5, 4-6, 6-4.
Three big names had exited on Tuesday, with holder Belinda Bencic, third seed Elina Svitolina and Australian Open champion Sofia Kenin all going out.
Top seed Simona Halep plays her opener later against fan favourite Ons Jabeur of Tunisia.
Pliskova pegged back Mladenovic after the Frenchwoman earned only her first main-draw win of the season in the first round.
“It’s always a tough one against her. We played in Australia, so I knew what to expect,” Pliskova said.
“I was not playing amazing but still, even with a couple of mistakes, I didn’t give up.
“The score looked a little bit easier than it really was, we had a couple of tough games.”
Muguruza had to struggle two days after beating Kim Clijsters in the Belgian’s first WTA match since 2012 after announcing a surprise comeback aged 36.
“There’s a lot of things that I could have done better,” two-time Grand Slam champion Muguruza said. “But I’m excited that I gave myself another opportunity to be in the quarters.”
Last month’s Australian Open finalist added: “I’m just happy that I get these tough matches.
“Honestly, the difference is very, very small, I’m just pleased to go through.”
Muguruza secured her place with a break in the final game as she converted her first match point.
She will bid for a semi-final place on Thursday, taking on Jennifer Brady, a 4-6, 6-4, 6-1 winner against Marketa Vondrousova.