Fourth seed Radwanska, who is yet to drop a set in 2013, maintained her impressive form with a routine 6-3 6-3 win over Irina-Camelia Begu on Rod Laver Arena.
Angelique Kerber, the No 5 seed, was rarely troubled as she beat Lucie Hradecka 6-3 6-1 although the German claims the match was harder than it looked.
"She's a tough opponent and you need to be ready for the whole match because she's playing the ball very hard and deep in the court," Kerber said.
"I was just trying to move well and play my game. I'm happy that I won in two sets."
Li Na, seeded six in Melbourne, found life slightly harder during her straight-sets victory over Olga Govortsova.
Li, a finalists in 2011, had trailed 5-3 in the second set but she rattled off four successive games to clinch a 6-2 7-5 win.
Fellow seeds Marion Bartoli, Julia Goerges and Ekaterina Makarova also progressed in straight sets.
Bartoli, the No 11 seed, beat Vesna Dolonc 7-5 6-0, 18th seed Goerges recorded a 6-3 6-2 triumph against Romina Oprandi, while Makarova, ranked 19, edged out Stephanie Foretz Gacon 6-3 6-3.
However three seeds did crash out, with Dominika Cibulkova, Klara Zakopalova and Tamira Paszek failing to advance.
Cibulkova, the 15th seed, was stunned 7-6 (8-6) 6-4 by qualifier Valeria Savinykh, No 23-ranked Klara Zakopalova was routed 6-1 6-0 by Kirsten Flipkens, while Madison Keys thumped 30th seed Paszek 6-2 6-1.