Kazakhstan play last year's runners-up Poland, led by women's world number two Iga Swiatek, in Saturday's other semi-final in Sydney.
Muchova, who suffered a career-threatening wrist injury and missed 10 months of tennis before returning last summer, made her case to be taken seriously at the upcoming Australian Open.
The 28-year-old, ranked 22 in the world to Paolini's four, defeated the Italian 6-2, 6-2 to give the Czechs one foot in the last four.
A gripping fourth game of the second set lasted more than 10 minutes and was pivotal as Muchova finally held serve, before breaking her opponent to love for 4-1.
Muchova now boasts a 5-0 record over Paolini.
"I really wanted to bring a point to the team so I was trying to stay focused," Muchova said.
"Jasmine is an unbelievable player. It was a really tough match. I knew I had to go until the end."
Tomas Machac was then equally ruthless in the men's singles rubber with a 6-1, 6-2 romp in 54 minutes over Flavio Cobolli.
It gave the Czechs an unbeatable 2-0 lead in the quarter-final.
Machac, who is 25th in the world, joked he "was playing like Novak (Djokovic)".
"This is the highest I can play. I'm really happy I managed to play this kind of match today," he said.
"I was surprised how great I played with no mistakes. It was the key to the match for sure."
The Czechs will face a United States team led by Coco Gauff and Taylor Fritz for a place in Sunday's final.
The Australian Open, the first Grand Slam of the year, starts in Melbourne on January 12.
