With the victory Sharapova, who lost in the final last year to Serena Williams, sets up a possible final four showdown with the world number one. (Agencies)
Williams, a six-time winner on the Miami hardcourts, takes on fifth-seeded German Angelique Kerber in another quarter-final clash later on Tuesday.
Sharapova, who has come up short in the Miami final each of the last three years, dropped her opening serve to Kvitova but that would be the only time the entire match.
The fourth-seeded Russian took control with a break to get back on level terms at 4-4 and then again to close out the first set. Sharapova then dominated the second set, storming through the first five games before a reeling Kvitova held her serve.
"I didn't have a good first few games, so I was happy that I was steady, that I kept trying to do the right thing, kept trying to be aggressive," said Sharapova. "I think that paid off as the match went on because I made a few too many unforced errors in the beginning."
Every time Sharapova has advanced as far as the quarters at Crandon Park she has reached the finals but could find a massive hurdle in her way if Williams gets past Kerber.
Sharapova and Williams, who have both achieved a career grand slam and held the number one ranking, were expected to develop into one of the great rivalries in women's tennis.
But it has not quite worked out that way with Williams dominating the series winning 15 of 17 career meetings including the last 14.
The two have clashed three times on the Miami hardcourts, Williams winning all three.
"It's no secret that she's been a big challenge of mine, an opponent that obviously I would love to beat," said Sharapova, looking ahead to a possible rematch. "There are certainly ways that I need to step up in certain situations that I haven't been able to do in the past against her.
"But it's great that I have come to that stage and have the opportunity to play her again."
With the victory Sharapova, who lost in the final last year to Serena Williams, sets up a possible final four showdown with the world number one.