Germany's Sabine Lisicki and Russia's Svetlana Kuznetsova were also winners, beating Dominika Cibulkova and Nadia Petrova respectively.
Russia's Svetlana Kuznetsova , seeded 14, made it safely through to round three after a 7-5 6-3 victory over Spaniard Maria Jose Martinez-Sanchez.
Russia's Svetlana Kuznetsova battled through to a 7-6 1-6 6-2 victory over former world No. 1 Caroline Wozniacki, though both players benefited from a heat break before contesting the deciding set.
Sharapova's compatriot Svetlana Kuznetsova produced the day's biggest shock by registering a comfortable 6-1 6-2 third-round win against Radwanska, who eliminated former world No. 1 Venus Williams on Wednesday.
In the women's singles Svetlana Kuznetsova is the defending champion but faces stiff competition in the face of the Williams sisters, as well as four-time French Open champion Justine Henin, who is competing for the first time since coming out of retirement.
Wozniacki, seeded 10th, beat Ukraine's Lesia Tsurenko 6-4 6-3 while Kuznetsova overcame Spain's Carla Suarez Navarro in three sets 6-2 4-6 6-3.
But Kuznetsova's compatriot, 10th seed Anastasia Pavlyuchenko, was knocked out of the tournament by Kazakhstan's Ksenia Pervak .
That, coupled with Kuznetsova's failure to take advantage of two break points in the following game, marked the effective end of her resistance.
Denmark's Caroline Wozniacki will face Svetlana Kuznetsova of Russia in the last 16 after both women won their third round matches on Saturday.
But two-time grand slam champion Svetlana Kuznetsova overcame Jankovic's fellow former world No. 1 Ana Ivanovic 6-2 2-6 6-4 to give the four-time champions hope of a rematch of last year's final.
He was joined on the withdrawal list by Thailand's Paradorn Srichaphan and Russian women Svetlana Kuznetsova and Nadia Petrova.
Safina beat Kuznetsova in last year's final and Monday's matches were their first in the tournament as the top eight seeds all received first round byes.
In Friday's third and final match, Slovakia's Daniela Hantuchova beat world number two Svetlana Kuznetsova 7-6 6-0 in a consolation match between the two eliminated players.
The American's hopes of reaching the last four now depend on Kuznetsova beating her fellow Russian Dementieva on Friday so all three players are left with one victory, with the player with the best record going through.
Elsewhere, second seed Venus Williams faces Swiss veteran Patty Schnyder, while defending champion Svetlana Kuznetsova of Russia opens her campaign against Romania's Sorana Cirstea.
The Russian, who upset French Open champion Svetlana Kuznetsova in the second round, progressed after beating Slovakia's Dominika Cibulkova 4-6 6-1 6-1.
Svetlana Kuznetsova gave Russia, beaten by Italy in last year's semifinals, a 1-0 lead when she defeated former world No. 1 Ana Ivanovic 6-1 6-4.
Kuznetsova has been a fixture in the upper reaches of the women's game since winning the US Open aged 19 but had struggled to live up to that early achievement, having been comfortably beaten by Justine Henin in the 2006 final in Paris.
French second seed Amelie Mauresmo overcame stubborn Russian fifth seed Svetlana Kuznetsova 7-6 4-6 6-2 and plays Australia's Alicia Molik for the other final place.
And there was a third shock when yet another Russian, French Open champion and fifth seed Svetlana Kuznetsova lost 7-5 4-6 6-3 to Germany's Andrea Petkovic.
Safina's defeat follows the first-round exits of big stars Justine Henin, Maria Sharapova and Svetlana Kuznetsova.
Second seed Svetlana Kuznetsova was also tested, trailing 2-5 in the first set to Bulgaria's Tsvetana Pironkova before triumphing 7-6 (7-0) 6-2.
Her next match could be her greatest challenge: a quarterfinal showdown with Svetlana Kuznetsova, a former champion here and one of the few players who can match Williams's power, assuming she's on her game.
Russian seeds Svetlana Kuznetsova, Anastasia Pavlyuchenkova and Maria Kirilenko also went through, with the latter to face Canada's Aleksandra Wozniak after eliminating Australia's Jarmila Gajdosova.
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