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Anderson won his second career title, to go with a triumph on home soil in Johannesburg last year.
The big-serving South African couldn't convert any of his eight break chances in the second set, but he took control early in the tiebreaker to finish off the victory in just under two hours.
"Both of us were a little nervous at the start of match, so I had to find my rhythm," said Anderson, who saved three match points in a quarter-final victory over Andy Roddick, then defeated top-seeded John Isner in the semi-finals.
"I think at the end, I felt I was mentally composed throughout (the tournament). I didn't let any patches of bad tennis affect my mindset."
Matosevic, ranked 173rd in he world, was playing in his first ATP final.
He was bidding to become the second player this year to come through qualifying and win a title, after Jarkko Nieminen in Sydney in January.
He admitted he felt a little flat, a day after notching a first ATP semi-final victory in his first attempt.
"My energy levels were pretty low," Matosevic said. "I just couldn't serve well today(Sunday), but credit to Kevin. He was the better player today(Sunday).
Although his run through qualifying to the final was impressive, Matosevic was clearly disappointed that he couldn't make the most of his chance.
"Before the week, if you told me that I'd make the final, I'd be the happiest guy in the world," he said. "Then when you get there and you play the match - I feel like I was just a few points from winning the match or turning the match, but I just couldn't do it. It can only help me I guess."
