Davenport won her quarterfinal match when Caroline Wozniacki retired in the second set, trailing 6-0, 4-2. Peer won for the seventh time in her last eight matches here by rallying for a 3-6, 6-1, 6-3 decision over Sofia Arvidsson.
Peer reached the finals of this tournament last year before losing to Venus Williams.
Davenport will face Marina Erakovic in the semifinals. Erakovic advanced by defeating Alla Kudryavtseva 4-6, 6-3, 6-3.
Olga Govortsova earned a match against Peer by winning over Julia Goerges 7-6 (7-5), 6-2.