Radwanska had no answer to the 26th seed, who rolled to a 6-0 6-3 win in barely an hour.
Lucic-Baroni also beat Radwanska at the Australian Open in January, in the second round en route to the semi-finals, where she eventually fell to Serena Williams.
Radwanska, speaking about Lucic-Baroni, told the WTA:
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. 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.
Another high seed had a fright, number six Garbine Muguruza overcoming a slow start to beat China's Zhang Shuai 4-6 6-2-6-2 in over two hours.
"Since I've started the year, I've had a lot of matches like this, and I'm expecting that every time I go on court," Muguruza said.
"A win is a win, I don't wish to have matches this tough every day, but I'm very happy with the way I'm facing them.”
It was Muguruza's second victory over Zhang in barely a month, after their match in Doha in February that also went three sets.
Second seed Karolina Pliskova's match went according to form, the Czech beating Kazak 27th seed Yulia Putintseva 7-5 6-3.
But 17th seed Anastasia Pavlyuchenkova was sent packing, beaten 4-6 6-0 6-3 by American Bethanie Mattek-Sands.
12-Caroline Wozniacki (Denmark) beat Sorana Cirstea (Romania) 6-4 6-2
15-Barbora Strycova (Czech Republic) beat Jana Cepelova (Slovakia) 6-2 6-4
26-Mirjana Lucic-Baroni (Croatia) beat 5-Agnieszka Radwanska (Poland) 6-0 6-3
6-Garbine Muguruza Blanco (Spain) beat 30-Zhang Shuai
Read the original article on Eurosport: Lucic-Baroni destroys Radwanska for second time this year