The first game of the match was interrupted for about 30 minutes by rain and Sharapova, the seventh seed from Russia and last year's losing finalist, was forced to save three break points before and after the interruption. (Agencies)
But from then on it was one-way traffic with Sharapova devouring the Argentine's serve and despatching winners with ruthless aplomb. She won the match on her first match point when the Argentine hit long.
Sharapova will play Samantha Stosur of Australia, the 19th seed, in the last 16. She has a 13-2 record against Stosur.
"I started off a little bit nervous, and I think she had another two break points when we came back after the rain. It was great to win that game, obviously get the advantage, and follow through with that," Sharapova said.
"I thought as the match went on I started playing better and better."
Ormaechea did not win a point on her second serve in the whole match and won only 37 percent of points on her first serve.
Sharapova's path through the draw has been cleared by the early dispatch of defending champion Serena Williams, who was in her quarter of the draw, second seed Li Na and, on Friday, the third seed Agnieszka Radwanska.
She sounded quietly confident ahead of the meeting with Stosur but added: "I believe this is one of her favourite surfaces. She has a great serve, she uses the court extremely well, moves well on it."
Stosur said: "I know what it takes, I know I have to play very well against her. I know there are certain things I have to do well and if I don't, then it makes life very, very tough."
The first game of the match was interrupted for about 30 minutes by rain and Sharapova, the seventh seed from Russia and last year's losing finalist, was forced to save three break points before and after the interruption.