Martinez will next take on Patty Schnyder, who beat Daniela Hantuchova 6-7 6-3 7-6 on Friday.
Sharapova needed two attempts to serve out the match before setting up a clash with Patty Schnyder.
Srebotnik now faces Swiss 10th seed Patty Schnyder , who beat France's Emilie Loit 7-6 (7-4) 5-7 6-2.
Meanwhile, in the women's event, Australia's Samantha Stosur set up a clash with Venus Williams after defeating Swiss Patty Schnyder 7-6 6-2.
It means sixth-seeded Patty Schnyder moves into the quarter-finals, along with Eleni Daniilidou, of Greece, who beat Czech Klara Koukalova 6-4 6-1.
Clijsters, who got married soon after retiring and gave birth to a baby daughter in February 2008, will next play old rival Patty Schnyder.
Fourth seed Venus followed up her opening win over Patty Schnyder with another routine straight-sets victory, defeating Israeli 16th seed Shahar Peer 6-3 6-4.
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.
In the remaining quarter-finals, Svetlana Kuznetsova beat Patty Schnyder 6-3 6-4 and will face top seed Justine Henin, who thrashed Elena Daniilidou 6-0 6-2.
Williams, 26, will play in the quarter-finals on Friday against the winner of Thursday's second-round match between Russia's Alisa Kleybanova and Swiss fifth seed Patty Schnyder.
The American second seed was still on court well past midnight and, on her least favorite clay-court surface, was sent packing 6-2 2-6 6-1 by Swiss Patty Schnyder.
Slovakia's Daniela Hantuchova, the 10th seed, was thrashed by Danish teen Caroline Wozniacki, Polish eighth seed Agnieszka Radwanska went down to Italian Francesca Schiavone, and Swiss number 13 seed Patty Schnyder was beaten by Austrian Sybille Bammer.
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