As the mercury rose at a sweltering Olympic Park, the top seed turned up the heat on her opponent, overcoming an early break to eventually cruise to a 6-4 6-3 win.
While much attention has focused on Serena Williams in the lead-up to the Australian Open, the Pole has quietly built up an enviable winning streak this year.
Radwanska took out the Auckland tournament last week without losing a set, the 23-year-old now enjoying a six-game unbeaten run.
She enjoyed a breakout 2012 when she reached her first grand slam final at Wimbledon and, at one stage, held the world No.2 ranking.
Equally impressive in Tuesday's early matches was Sara Errani.
The Italian third seed enjoyed a 6-1 6-1 win over Russian Maria Kirilenko.