Peer, the second seed, won a tight match against fourth-seeded Olga Govortsova of Belarus 7-6 (7-5), 6-2, twice rallying from a break down in the first set.
She won last week's Guangzhou (China) Women's Open and has not lost a set at Taskent.
"I'm happy I'm playing better tennis after every match," Peer said. "I just want to keep going that way (Sunday)."
The unseeded Amanmuradova, a Tashkent native, was a surprise 6-4, 7-6 (7-3) winner over top-seeded Yaroslava Shvedova of Kazakhstan, sending a home crowd into euphoria.
"I was always under pressure but I'm happy to have survived," Amanmuradova said. "It's a big responsibility to play in front of your home crowd, but I was relaxed and played well."
Sunday's Peer-Amanmuradova winner earns $37,000.