Karlovic, the defending tournament champion, ran his Slazenger winning streak to eight matches with a 6-3 3-6, 6-4 victory over seventh-seeded Andreas Seppi. Karlovic fired 19 aces in beating Seppi.
Verdasco, seeded third, survived a tough match with fifth-seeded Gilles Simon, eventually wining 6-3, 2-6, 6-3.
Also Thursday, eighth-seeded Gael Monfils took out Vincent Spadea 7-6 (7-4), 6-2 and Marin Cilic whipped Thomas Johansson 6-1, 6-1.
Verdasco is paired against Cilic, whom he beat in their only career meeting, and Karlovic goes against Monfils, to whom he lost in their only career meeting.
Friday's winners advance to the tournament championship match Saturday.
Notable deaths of 2014 [PHOTOS]