World number 10 Fritz raced through the first set before allowing 25-year-old Tirante back into the contest in his first ATP Tour final.
The experience of former US Open runner-up Fritz paid, however, in the deciding tie-break, in his last match of the year after failing to qualify for the ATP Finals.
Fritz claimed the first indoor title of his career in his sixth final of the season.
He is guaranteed to finish the year inside the top 10 for a fifth straight season.