Cilic, Verdasco through in Umag
World number 15 Cilic comfortably beat USA's Wayne Odesnik 6-4 6-0 to reach the semi-finals.
There he will face the man who beat him in last year's final, Alex Dolgopolov, after the Ukrainian beat Argentina's Carlos Berlocq 6-4 6-4.
In the other half of the draw, top-seeded former champion Verdasco needed little more than an hour and 20 minutes to see off Russia's Andrey Kuznetsov 6-2 6-2.
The Spaniard will face compatriot Marcel Granollers for a place in the final after he fought back to beat Mattias Bachinger 1-6 6-3 7-5.