The Polish world number two and five-time Grand Slam winner could not force a single break point and saved two of the seven she faced as she fell in one hour and six 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.
The world number four secured two more breaks in the second set and wrapped up victory at the first time of asking.
"Obviously she wasn't maybe playing her best tennis, but I think I made her uncomfortable," said Gauff. "She is very talented and can make you run and move you around the court. And I just tried to not do that today."
Three straight wins against Swiatek
Gauff beat Swiatek at the 2025 United Cup and in the WTA Finals last year, both on hardcourt, but the American had never previously defeated the four-time French Open winner on clay.
"I think the previous times we played on clay I don't think I had a win against her yet..." said Gauff.
"Obviously on clay she's a different player, but clay is one of my better surfaces too, and I thought if I can beat her on hard I can beat her on clay."
Last year's runner-up Aryna Sabalenka faces in-form Elina Svitolina in the second semi-final later Thursday.