Muchova had never beaten world number three Gauff in six matches, including a loss in the fourth round of this year's Australian Open, but prevailed 6-3, 5-7, 6-3 to reach the Stuttgart semi-finals for the first time.
The 12th-ranked Muchova will face Elina Svitolina for a place in the final.
After ensuring Gauff exited the tournament in the quarter-finals for the third straight year, Muchova said she tried not to let the daunting record impact her preparation.
"It was a great fight. I'm just happy that I finally, finally beat her," Muchova said.
"This was actually our first match on a clay court. On clay, we were 0-0 in the matches - I tried to keep it positive."
Earlier on Friday, fourth seed Svitolina moved past Czech Linda Noskova 7-6(2), 7-5 to book her semi-final spot.
The in-form Ukrainian has now reached five semi-finals this season.
Svitolina told reporters she had rediscovered her fighting spirit after a difficult 2025.
"I had a really difficult end of last year, struggling a bit mentally," Svitolina said.
"I think my fighting spirit is back this year. I'm very pleased with that."
Later on Friday, third seed Iga Swiatek takes on rising star Mirra Andreeva while top seed Elena Rybakina faces Leylah Fernandez.