
The Frenchwoman next faces Serena or Venus Williams, who play their semi-final later.
The 25-year-old Razzano continued a remarkable run this week that has included upset victories over second seed Dinara Safina and number five Vera Zvonareva.
Sixteenth seed Kanepi, who beat world number three Jelena Jankovic on her way to the semis, broke serve in the opening game but looked weary for most of the match.
Razzano struck the ball more positively and was also more mobile than her opponent. After breaking back for 1-1 she reeled off the next seven games to take the first set and lead 2-0 in the second.
The Frenchwoman had a break point to lead 3-0 in the second but netted her return and Kanepi went on to hold with an ace.
Kanepi then broke for 2-2 when her opponent double-faulted before netting a weak forehand.
Razzano, however, quickly regained control and claimed the final four games for the loss of three points to wrap up the match in 63 minutes.
"It was me who was the boss today," Razzano told reporters. "I wanted to do my best to reach the final."
Kanepi said she felt more tired in her quarter-final but was simply out of form.
"Almost nothing went right. The serve didn't work that well and the baseline game wasn't that good either," she said.
"She also played very well and played some great shots. It's very disappointing but I just have to learn from my mistakes and move forward."
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