The seventh-seeded Anderson out-battled the Australian 6-4, 7-6 (7-2) in 1 hour, 57 minutes on the hard courts at Delray Beach Stadium and Tennis Center.
It was the second career ATP title for Anderson, 25, whose only other win came last season in his hometown of Johannesburg.
The 26-year-old Matosevic, meanwhile, surrendered five double faults while appearing in his first career ATP Tour final.
He was the first qualifier to reach the Delray Beach final since a 2009 run by Evgeny Korolev that resulted in a championship.
Swim Week Miami Beach 2014 [PHOTOS]