The top-seeded Dementieva, ranked No. 4, dropped her serve in the opening game but broke fifth-seeded Peer to level at 2-2 in what seemed a close match. But she then reeled off nine straight games to take charge of the match and to improve to 5-1 in her career against Peer.
"We've played before so I knew what I wanted to do on court,'' Dementieva said. "It looked easy, but it was not that easy. She is a very tough player.''
Peer was the subject of a protest outside the tournament venue by about 20 people, objecting to her presence at the tournament given Israel's military action in the Gaza Strip.
"I'm sure it was a tough day for her because of the situation in her country,'' Dementieva said. "I'm sure it was not easy to play for her. I just know she can play better tennis next week.''
Dementieva's semifinal opponent will be France's Aravane Rezai, an Iranian-born Muslim and friend of Peer. Rezai beat unseeded Romanian Edina Gallovits 6-3, 6-2.
"I'll try to move her around and mix it up a lot, and not give her short balls, because she likes to step into the court and make a winner,'' Dementieva said.
Peer had nothing to say to the protesters who had previously asked her to withdraw from the tournament.
"I'm not the government of Israel and I'm not representing Israel as a politician,'' she said. "I'm a tennis player and that's what I represent now.''
Second-seeded Caroline Wozniaki of Denmark, ranked 12th, fell to unseeded Russian Elena Vesnina 6-3, 0-6, 6-3. Vesnina will meet unseeded Anne Keothavong of Britain in the semifinals.
Keothavong defeated Japanese qualifier Ayumi Morita when Morita retired with an injury in the second set after losing the first set 6-0.
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