Haase, who came off his third career final in Gstaad last week, broke the Spaniard at 5-4 in the second set and came back from a break down in the third.
After winning in 2011 and '12, the Dutchman is now 12-0 at the event.
He will play eighth-seeded Marcel Granollers of Spain, who beat Leonardo Mayer of Argentina 6-3, 6-1 to reach his first semi-final of the season.
Also, second-seeded Juan Monaco defeated Daniel Gimeno-Traver of Spain 6-2, 3-6, 6-4.
Monaco will next face Albert Montanes of Spain.
Results from day five of the ATP Kitzbuehel Cup (x denotes seeding):
Marcel Granollers (ESP x8) bt Leonardo Mayer (ARG) 6-3, 6-1
Robin Haase (NED) bt Fernando Verdasco (ESP x3) 4-6, 6-4, 6-3
Albert Montanes (ESP x7) bt Dominic Thiem (AUT) 6-4, 6-3
Juan Monaco (ARG x2) bt Daniel Gimeno (ESP) 6-2, 3-6, 6-4