Craybas, who opened the tournament with a 6-0, 6-0 whitewash of Meng Yuan, defeated Peer, 6-2, 7-5, by successfully defending 15 of 18 break points she faced.
She moves into the hard-court tournament semifinals for the third time this year. She is paired Saturday against unseeded Samantha Stosur, who defeated Ekaterina Makarova, 6-3, 6-4. The two have never before met in a WTA match.
Top-seeded Maria Kirilenko, who was the 2007 Korea Open runner-up, made the semifinals with a 6-3, 6-2 win over fifth-seeded Pauline Parmentier. The fourth quarterfinals saw third-seeded Kaia Kanepi defeat Yanina Wickmayer, 6-1, 6-4.
Kirilenko won the only time she played Kanepi, taking a three-set match early this year.
The 2008 Korea Open championship, to be decided Sunday, is worth $22,900.