Robredo took a first-set tiebreaker and then bounced back from a sub-par second set to post a 7-6 (8-6), 4-6, 6-3 victory over Anderson, saving all four break points he faced down the stretch.
The win was the 10th on clay courts for the 30-year-old Spaniard, but his first since the Santiago event in February 2011.
He improved to 11-7 all-time in finals.
Anderson fell to 2-3 in championship matches.
Notable deaths of 2014 [PHOTOS]