Petrova went 4-3 up in the all-Russian match with a break in the seventh game of the first set, but Dementieva won three consecutive games to take the set. Dementieva was leading 4-1 in the second set but Petrova came back strongly and won five consecutive games to level the match at one set each.
In the third, Dementieva again took a 4-1 lead but Petrova rallied back to 4-4 and then both players held their serves to force a tiebreaker which Dementieva won on her third match point.
"It was not an easy match,'' Dementieva said. "There were many missed chances for me today.''
Another Russian, Vera Zvonareva also advanced, beating Dominika Cibulkova of Slovakia, 7-5, 6-4.
In the semifinals, Olympic champion Dementieva will play the winner of the quarterfinal match between top-ranked Jelena Jankovic and Flavia Pennetta of Italy.
"I will likely meet Jankovic,'' Dementieva said. "Today she is the strongest player in the world. She's playing terrific tennis and has just won back-to-back titles on different surfaces and in different parts of the world. It won't be an easy match. It will be interesting for me to challenge her.''
Seventh-seeded Zvonareva saved five break points in the tenth game of the first set before breaking Cibulkova in the next game to win the set. Two breaks early in the second set secured her a berth in her first semifinal after five quarterfinal appearances in her home town event.
In the men's quarterfinals, veteran Fabrice Santoro won the first set 6-3 and was 2-0 up in the second when his fellow Frenchman Paul-Henri Mathieu, seeded fourth, retired because of illness.
"The first set was my best performance here so far,'' Santoro said. "I was serving well while he (Mathieu) was obviously out of form and could not return at full strength.''
Santoro, who will turn 36 in December, won his only title this season in Newport in July. He will be playing in his third semifinal this season.
Mischa Zverev of Germany rallied from 5-1 down in the third set to advance to his first career ATP Tour semifinal with a 6-4, 3-6, 7-5 victory over Viktor Troicki of Serbia.
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