Verdasco battled past No. 2 seed Nicolas Almagro 6-4, 7-6 (7-5) on the red-clay surface, eliminating the two-time former champion.
Almagro had won 10 of his previous 11 matches, all on clay. He captured the ATP Tour stop in Sao Paulo two weeks ago and lost in the Buenos Aires final last week to David Ferrer.
Stanislas Wawrinka will meet Verdasco in the semifinals after downing Jeremy Chardy 7-5, 6-1.
Ferrer, seeded No. 1 in this tournament, cruised into the semifinals with a 6-2, 6-4 decision over Pablo Andujar.
2014: The Year in Music [PHOTOS]