Muchova improved to 5-0 in her career against Paolini, who was a finalist at the French Open and Wimbledon last year.
Tomas Machac then beat Flavio Cobolli 6-1, 6-2.
Muchova and Machac will next face Americans Coco Gauff and Taylor Fritz, respectively.
Iga Swiatek’s Poland plays Kazakhstan in Saturday’s other semifinal of the mixed team event.
The United Cup is a warmup for the Australian Open, which starts Jan. 12.
