Daniela Hantuchova of Slovakia, Romina Oprandi of Switzerland and Maria-Teresa Torro-Flor of Spain also moved into the last four. The top-seeded Hantuchova received a walkover from Peng Shuai of China, who had a left thigh injury, Oprandi defeated third-seeded Yvonne Meusburger of Austria 6-4, 6-4, and Torro-Flor edged Polona Hercog of Slovenia 7-6 (3), 7-6 (5).
The fifth-seeded Muguruza won seven straight games against Peer to clinch the first set and lead 5-0 in the second.
The Spaniard is enjoying a breakthrough season, as she clinched her first WTA title in January at the Hobart International and finished runner-up at the Brazil Cup in March.
Peer made five double faults and was able to hold serve only once.
Muguruza will face Torro-Flor, who wasted a 4-2 lead in the last set but rallied from 5-3 down in the final tiebreaker. Hercog failed to serve out the first set at 5-4 and double-faulted seven times.
Oprandi reached her first semifinal since the Brussels Open in May 2013 and will play Hantuchova. The Swiss player rallied from a 3-0 deficit to lead 5-3 in the first set, and broke Meusburger for a 2-1 lead in the second.
Meusberger made seven double faults and converted only one of five break points.