The Russian was on court for just 51 minutes against the world number 75, who crumbled on the clay of Court Philippe Chatrier.
Sharapova – searching for a second success at Roland Garros following her 2012 triumph – hit 23 winners and won 88 per cent of her first-service points in a completely one-sided affair.
Ormaechea struggled to cope with the power of the seventh seed, the 21-year-old failing to win a single point on her second serve.
After a shaky start from the underdog, there was to be no let up as Sharapova ruthlessly dispatched almost every opportunity that came her way.
Sharapova broke to love on Ormaechea’s final two service games as the match came to an abrupt end.
Stosur, seeded 19th, should provide a sterner test for Sharapova in round four.
The Australian toppled ninth seed Dominika Cibulkova 6-4 6-4 on Friday.
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