The sixth-seeded Sharapova needed a little over an hour and a half to defeat her fellow Russian, keeping alive her dream of winning the tournament for the third year in a row.
Polish world No. 3 Radwanska was rarely troubled in wrapping up a 6-3, 6-2 win over Italy's Roberta Vinci.
Svetlana Kuznetsova of Russia rallied from a 5-2 first-set deficit to edge second seed Simona Halep of Romania 7-5, 7-6 (4) in the late match.
Fifth seed Jelena Jankovic rallied after losing the first set to beat Flavia Pennetta of Italy 3-6, 6-2, 6-3 for a quarterfinal against Alisa Kleybanova, who upset the third-seeded Petra Kvitova on Wednesday.