The 22-year-old, who won the Stockholm Open in October for his first title victory, claimed the first-set in a tiebreak but Anderson broke in the second game of the next and comfortably held serve to level the match at a set apiece.
Anderson carried the momentum into the third with another early break but handed back the initiative with a double fault on break point in the eighth game of the deciding set.
Dimitrov, who beat Wimbledon champion Andy Murray in the semi-finals, held on to take the decider into a tiebreak and completed the victory on his first match point to improve his head-to-head record against the South African to 4-1.
It was a second heartbreaking loss in as many weeks for Anderson, who also lost to Marin Cilic in the Delray Beach Open final last Sunday.
"Right now it's really disappointing... to come so close. It was possibly a match where I felt I was going to get it," Anderson told reporters. "I'm going to have to move on, need to take positives and take belief.
"I know it's difficult but it's not an easy sport. You have got two options - either to get down or get even more motivated."
In the women's tournament played at the same venue, top seeded Slovakian Dominika Cibulkova battled past American Christina McHale 7-6 (7-3) 4-6 6-4 to win her fourth career title.
The victory will move Cibulkova a place higher to number 11 from her previous career-high world ranking when the new standings are released on Monday.
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