The seventh-seeded Cilic, who won the Zagreb Indoor event two weeks ago, battled past No. 4 seed Anderson 7-6 (8-6), 6-7 (7-9), 6-4 in a match that went more than 3 hours.
It was the 11th overall career title for Cilic, who improved to 4-1 all time against the fourth-seeded Anderson.
The South African came up short in a bid for his third career title.
Susan Sarandon 'very excited' about daughter's pregnancy
Dennis Rodman pledges to end trips to North Korea