Sharapova was too strong for Ekaterina Makarova - the conqueror of Serena Williams in the previous round - while Kvitova struggled to get past Sara Errani.
Although the number two seed may have turned in an error-filled display in seeing off the world number 48 she has won her last two meetings with Sharapova, including the Wimbledon final last year.
And the Russian is expecting another tough encounter.
"I've lost to her the last couple of times - including obviously the big one at Wimbledon where she played really well," she said.
"I think she's the one to beat right now, she's playing the best tennis of her career, coming off so many wins last year. I'm looking forward to the match-up.
"I don't like losing so many times in a row so I'll certainly be going out there and trying to play my best."
Sharapova was the more impressive of the two today, a ruthlessly efficient display accounting for Makarova, who acquitted herself well in her first grand slam quarter-final.
"It was solid today," said Sharapova.
"I thought she was going to play well coming off a big win, probably the biggest of her career.
"It was really important for me not to give her too much of a look at the open court.
"I really wanted to take advantage of my game and improve from the previous match and I think I stepped up when I had to."
In a match of hard-hitting baseline rallies, fourth seed Sharapova possessed the greater accuracy, particularly at the key moments, to move through 6-2 6-3.
The 2008 champion here, Sharapova has made smooth progress through the draw with her only dropped set coming against Sabine Lisicki in round four.
Indeed, the only shadow being cast over her tournament is the issue of grunting which has again been raised with Sharapova and her fellow semi-finalist Victoria Azarenka singled out as the worst offenders.
Agnieszka Radwanska, beaten by Azarenka in the last eight yesterday, spoke out after her loss and expressed hope the WTA would take action.
When asked about Radwanska's comments, Sharapova snapped: "Isn't she back in Poland already?
"I've been the same over the course of my career. No one important enough has told me to change or do something different."