The 19-year-old Szavay, who won her first two singles titles and reached the U.S. Open quarter-finals last year, will meet top seed Anna Chakvetadze of Russia or Frenchwoman Marion Bartoli in Sunday's final.
Dementieva, seeded fourth in the indoor event, recovered from the loss of the first set to take the second easily.
The Russian opened up a 3-1 lead in the decisive set and served for the match, leading 5-4, but Szavay, seeded seventh, kept fighting to seal victory when her opponent hit a backhand long on set point.
(Reporting by Myrtille Rambion, writing by Patrick Vignal, editing by Alison Wildey)
