Knapp, the No. 8 seed, was on the court just 60 minutes in a 6-0, 6-1 win over Beck. She lost only nine points in seven games serving and didn't face a break point.
Knapp also won two-thirds of the points off Beck's serve, finishing off all five of her break chances.
She and Beck were the only seeded players to advance as far as Friday's quarterfinals.
Yvonne Meusburger gained a semifinals berth with a 6-1, 7-6 (7-1) decision over Arantxa Rus. Meusburger took 60 percent of the points in the match -- 62 percent when serving and 59 percent when receiving.
Elina Svitolina saved the four break points she had to deal with in a 6-3, 6-0 win over Patricia Mayr-Achleitner and Andrea Hlavackova, with six breaks, claimed a 6-3, 7-6 (7-4) victory over Lisa-Maria Moser in the other quarterfinals.
Meusburger will take on Knapp in the first semifinal Saturday. She's won both their previous meetings, including a pairing in the 2007 semifinals in Bad Gastein. Saturday will be the first WTA meeting between Svitolina and Hlavackova.