Swiatek will face world number two Aryna Sabalenka or American 13th seed Danielle Collins in the Rome showdown on Sunday.
Gauff saved two early break points in the first game and then broke Swiatek in the second for a 2-0 lead.
However, the Pole hit back and then broke the US Open champion at 4-4 before holding to take the first set 6-4 with a clinical backhand winner.
The second set went with serve until Swiatek broke the 20-year-old to lead 3-2 and eventually booked her spot in the final where she will bid for a third Italian Open title in four years.
Following her 11th straight win on clay, Swiatek could become only the third player in history to win the Madrid-Rome double after Dinara Safina in 2009 and Serena Williams in 2013.
Meanwhile, Gauff and New Zealand's Erin Routliffe will take on China's Saisai Zheng and Xinyu Wang in the semi-finals of the women's doubles on Saturday.
In the men's singles draw US 14th seed Tommy Paul came through a marathon match to beat Polish seventh seed Hubert Hurkacz 7-5 3-6 6-3 and reach the semi-finals.
Paul, who defeated defending champion Daniil Medvedev in the previous round, has yet to drop a set before the quarter-final, but Hurkacz managed to force the match into the decider before the American came out on top.
It was a match which went back and forth with 13 breaks of serve overall. The pair exchanged breaks early in the opening set, with Paul breaking twice to lead 3-2. With Paul serving for the set, Hurkacz broke again to make it 5-5.
Paul broke back immediately and held serve to take the first set. The American made a strong start to the second, breaking in the first game, but Hurkacz came back, breaking twice to force a third set.
This time it was the Pole who took an early 2-0 lead, but they again exchanged breaks of serve to make it 3-3 before Paul made the decisive break to go 5-3 up, and then saved six break points to wrap up victory.
Paul awaits the winner of the last quarter-final between Greece's sixth seed Stefanos Tsitsipas and Chilean 21st seed Nicolas Jarry.
Another Chilean, Alejandro Tabilo is already into the other semi-final and will take on German third seed Alexander Zverev.
- Reuters/RNZ