Verdasco, champion here four years ago, stormed past wild-card entrant Andrey Kuznetsov 6-2, 6-2.
Cilic, a finalist at this tournament last year, recorded eight aces while defeating Wayne Odesnik 6-4, 6-0.
Cilic's semifinal opponent will be Alexandr Dolgopolov in a rematch of the 2011 championship duel. Dolgopolov made it to the semifinals with a 6-4, 6-4 decision over Carlos Berlocq.
Marcel Granollers will take on Verdasco after coming from behind to down Matthias Bachinger 1-6, 6-3, 7-5.