The third-seeded American won 6-1, 6-4 in a match that began as a one-sided canter for Williams but ended as a battle with Peer threatening to extend the match into a third set.
Willimas will meet fourth seeded Victoria Azarenka of Belarus who eased past Poland’s Agnieszka Radwanska 6-3, 6-4.
Roddick through
Defending champion Andy Roddick was pushed for the second straight day before prevailing over Lu Yen-hsun 7-6, 6-4 on Thursday during the second round of the Memphis Championships.
"As well as I did some things tonight, if I want to move through this tournament I've got to do better on break points," Roddick told reporters. "I've very close to playing really well and it's just a matter of tighten up a couple things."
Roddick next faces fellow American Sam Querrey, who defeated Argentina's Leonardo Mayer 6-4, 6-0.
In the women's draw, top seed Maria Sharapova of Russia dispatched eighth seed Elena Baltacha of Britain 6-2, 7-5.
Sharapova will play fifth seed Petra Kvitova of the Czech Republic for a place in the final.
Second seed American Melanie Oudin failed to join Sharapova in the last four, losing to unranked Swede Sofia Arvidsson 6-1, 6-3. Arvidsson Briton Anne Keothavong in the other semifinal clash.
Bopanna-Coetzee in semis
Indian Davis Cupper Rohan Bopanna and Jeff Coetzee prevailed 4-6, 6-1, 21-19 over third seeds Mark Lopez and Tommy Robredo and storm into semifinals of the ATP World Tour event in Marseille, France. Bopanna and Coetzee will next play Julian Knowle of Austria and Robert Lindstedt of Sweden.