Cilic, the No. 2 seed, will face American Wayne Odesnik in the quarterfinals. Odesnik edged by Slovenian Blaz Kavcic 3-6, 7-5, 7-6 (7-3) in the second round.
Cilic finished second to Ukrainian Alexandr Dolgopolov in last year's event on the red clay at ATP Stadium.
In other action Wednesday, Italian Potito Starace, the 2010 Umag runner-up, extended fourth-seeded Spaniard Marcel Granollers to a third set before falling 6-4, 3-6, 6-3.
In a mild upset, German Matthias Bachinger defeated seventh-seeded Slovak Martin Klizan 6-0, 2-6, 6-4. Bachinger and Granollers will meet in Friday's quarterfinals.
On Thursday, top-seeded Fernando Verdasco of Spain, who won here in 2008, will go against Latvian Ernests Gulbis and Dolgopolov, the No. 3 seed, meets Italian Fabio Fognini.
2014: The Year in Music [PHOTOS]