Fifth-seed Agnieszka Radwanska had her bid to repeat her 2012 success at the Miami Open ended by Croatian veteran Mirjana Lucic-Baroni at Crandon Park.
But second-seed Karolina Pliskova fought past Yulia Putintseva of Kazakhstan 7-5 6-3 to move into the last 16 and Slovak Dominika Cibulkova also progressed with a comfortable two sets win over Belgium’s Kirsten Flipkens.
Lucic-Baroni is enjoying an unexpected upturn in her fortunes at the age of 35 and in January reached the semi-final of the Australian Open - 18 years after her previous appearance in the last four of a slam, in 1999 at Wimbledon.
The Croat was a teenage prodigy who appeared to have disappeared from the top tier of the sport but has fought her way back impressively in recent years and is now ranked 29th in the world.
The 6-0 6-3 scoreline emphasised her dominance over her Polish opponent on Saturday, as Radwanska acknowledged.
"She was playing unbelievable tennis today. She was very solid from the beginning, very aggressive, hitting everything with unbelievable speed. I couldn't do much," she said.
"The first set went so quickly, and in the second set I had chances, but I didn't come back and unfortunately I missed the chance to stay in the match. She was just too good today."
Spain's sixth seeded Garbine Muguruza is doing it the hard way in Florida this week.
After battling back to beat American Christina McHale in three, rain interrupted, sets on Friday, the Caracas born Muguruza had to pull out the stops again to deal with China’s Zhang Shuai 4-6, 6-2, 6-2 in just over two hours.
"It's very tough, especially the first round with players that you don't maybe play a lot. They are very good players as well. The difference is not that big. They play very well and you are in danger all the time," said Muguruza.
"I'm just going through these situations with the best attitude possible, being humble, trying to accept it, and find my way," he said.
The Spaniard will face the winner of Saturday’s scheduled later game between Romanian Sorana Cirstea and Caroline Wozniacki.