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 yesterday.
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 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."
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.
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