The Polish world number two and five-time Grand Slam winner could not force a single break point and dropped serve five times as she fell in 64 minutes.
Swiatek, usually excellent on clay, has struggled during her Madrid title defence.
She dropped sets against Alexandra Eala and Diana Shnaider, and then was dealt a bagel by Madison Keys in just 24 minutes on Wednesday.
However, the 23-year-old Pole bounced back strongly to defeat the American, but came undone against Keys' compatriot Gauff, who beat Swiatek for the first time on the red dirt.
Gauff, 21, broke in the third, fifth and seventh games to blow Swiatek away in the first set, converting her second set point.
She secured two more breaks in the second set and wrapped up victory at the first time of asking, on serve to love.
Last year's runner-up Aryna Sabalenka faces in-form Elina Svitolina in the second semi-final later on Thursday.