The second-seeded Russian had reached the previous three finals at Roland Garros, winning in 2012 and 2014, but could not handle her opponent's steely forehand.
Safarova, who had never progressed to the quarter-finals on the Paris clay in 10 previous attempts, hit 20 forehand winners to unsettle the former world number one on Court Philippe Chatrier.
She next faces 21st seed Garbine Muguruza after the Spaniard went through to the last eight for the second year in a row by defeating Italy's Flavia Pennetta in straight sets.
Sharapova, who had lost only one of her previous 24 matches at Roland Garros, dropped her serve in the third game but broke back in the eighth when her opponent double-faulted.
She then lost her fourth consecutive tiebreak of the season.
The Russian, who has five grand slam titles to her name, went 3-0 down in the second set but fought back to 3-3 after Safarova made a mess of a routine forehand at the net with the court wide open.
The Czech regained control and ended the contest on Sharapova's serve with a forehand winner.
(Editing by Tony Jimenez)
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