Second seed Thiem, who became the favourite after top seed Kei Nishikori was knocked out in the first round, did not lose a set the entire tournament.
Thiem, 23, came through at crucial moments in the final, breaking in the final game of both sets after he and Carreno Busta had exchanged an earlier break.
World number eight Thiem retained his perfect career record against the Spaniard, improving to 4-0.
The result prevented Carreno Busta from adding a singles title to the doubles he won with Pablo Cuevas on Saturday.
