The second-seeded Croat was in control throughout, hitting six aces and dropping serve only once. Brands wasted two break points for a 2-0 lead in the second set, and Cilic then won five games in a row.
"I played a very good match, I made almost no mistake at all," Cilic said. "It was a bit easier that I had expected, since this was my first match on clay after a while. I felt I was in control the whole time."
Cilic will face Wayne Odesnik after the American rallied to beat Slovenia's Blaz Kavcic 3-6, 7-5, 7-6 (3). Kavcic wasted a 5-1 lead in the third set and was later two points away from closing out the match at 5-4.