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.
The defeat effectively ends Schnyder's hopes of playing in the season-ending WTA Championships in Madrid next month.
Srebotnik now faces Swiss 10th seed Patty Schnyder , who beat France's Emilie Loit 7-6 (7-4) 5-7 6-2.
In Friday's final match, third seed Schnyder defeated Vera Zvonareva 7-6 (7-2) 6-4.
The Dane, who beat Schnyder on the way to winning the Ponte Vedra title last week, came through 6-2 7-5.
Rolf W. Schnyder, CEO of Swiss watch manufacturer Ulysse Nardin, unexpectedly died on April 14 after a short illness.
Sharapova broke early against Schnyder to lead 2-1 but failed to convert three set points on her opponent's serve at 5-3.
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.
The American wore the same self-designed black lace number she had unveiled against Schnyder, a see-through skirted bodice featuring a skin-coloured undergarment.
She again dropped her opening service game in the second set but completed six breaks of the Schnyder serve to record her victory.
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.
Sharapova immediately lost her own serve after breaking for 1-0 in the second set, but then broke again for a decisive 6-5 lead when Schnyder netted a forehand.
In a long and dramatic contest that lasted for two hours and 42 minutes, Schnyder recovered from losing the first set to outlast and ultimately out-power her seventh-seeded teenage opponent.
The world number four dispatched the challenge of Schnyder, from Switzerland, 6-2 6-2 in just one hour and 14 minutes after nearly a month out due to a knee injury.
Rolf W. Schnyder had acquired the family firm Ulysse Nardin in 1983, and since that time held the role of president and CEO at the helm of the manufacturer with its wealth of tradition.
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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