Buenos Aires-born Schwartzman fought back from 4-2 down to force a tiebreak in the third set.
The world number 19 held his nerve in a nail-biting tiebreak to condemn Thiem, who had won the title in both of his previous two appearances at the tournament, to his first defeat in the Argentine capital.
Schwartzman will take on Cecchinato in Sunday’s final after the Italian beat another Argentine, Guido Pella, 6-4 6-2.
(Reporting by Andrew Downie, editing by Pritha Sarkar)
