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The 2008 champion was thoroughly outplayed by the 24-year-old, who prevailed 3-6 6-4 6-1.
After Sharapova had taken the opening set in 39 minutes, Cibulkova raced into a 5-0 lead in the second. However, the 20th seed won just six of the next 22 points, allowing Sharapova to close the gap to one game.
Despite producing her fifth double fault of the day to surrender the first of two set points, Cibulkova was eventually able to stem the tide and level the match at one set all by holding to 30.
Sharapova received an off-court medical timeout, seemingly for a gluteal problem, before the final set and she began the decider poorly, making two double faults en route to losing the opening two games.
She double-faulted twice more in game three, but managed to survive two break points and secure a gritty hold.
Sharapova has now lost to Cibulkova in two Grand Slams, having exited the 2009 French Open with a 6-2 6-0 defeat at the hands of the 5'3" star.