The Pole produced a commanding performance to claim a 6-3 6-2 victory over her Czech counterpart at the WTA International hard-court event.
World number three Radwanska was always in control of a one-sided affair, never dropping serve and winning 80 per cent of points on her first serve in a fine display.
Italy's Roberta Vinci also enjoyed a straightforward win, defeating Russian qualifier Ksenia Pervak 6-3 6-3.
However, it was Vinci's compatriot Francesca Schiavone who demonstrated the most impressive performance of the day, crushing qualifier Vera Dushevina 6-0 6-2.
Schiavone did not allow Dushevina to win a game in the first set and, although the Russian avoided the dreaded 'double-bagel', she was not able to mount any kind of comeback.
Radwanska was the only Polish player able to provide the home fans with something to cheer about as Magdalena Frech and Magda Linette both succumbed to defeat.
Frech was soundly beaten 6-3 6-1 by Austria's Yvonne Meusburger, and Linette slipped to a 6-4 6-3 loss to Klara Koukalova.
Meanwhile, eighth seed Tsvetana Pironkova came from a set down to beat Andrea Hlavackova 4-6 7-5 6-1.
Hlavackova moved into the lead after breaking the Bulgarian twice in the first set, but Pironkova forced a decider by winning a frenetic second set that saw both players struggle to hold serve.
And Pironkova carried that momentum into the decider, which she claimed in 34 minutes to progress.
Fourth seed Alize Cornet of France was far more comprehensive in her 6-3 6-2 success against Vesna Dolonc of Serbia, and Spain's Silvia Soler-Espinosa easily overcame Japan's Misaki Doi 6-1 7-5.
Elsewhere in the draw, Slovakian qualifier Kristina Kucova moved into round two with a 6-1 6-1 triumph over Romanian Monica Niculescu.