The 19-year-old Argentine won his maiden title in Stuttgart, Germany, last week.
"These were two great weeks for me, really unbelievable,'' said Del Potro, who conceded 29 games in five matches in Kitzbuehel. "I can only dream that I will be able to play on at this level.''
It was Melzer's first final of the year. The Austrian is now 1-6 in finals, winning only in Bucharest, Romania, in 2006.
"I am very disappointed, obviously,'' Melzer said. "Everything went wrong today and he was just too good. It was a great tournament anyway as I'd never reached the final here before.''
Del Potro dominated the match with strong serves and attacking baseline play. He faced one break point in his opening service game, but conceded just three more points on serve during the rest of the first set and didn't drop a single point while serving in the second.
Del Potro's dominance put pressure on Melzer's service games. The Austrian was broken twice in the opening set and three times in the second, and received treatment on a left ankle injury in-between sets.
At 2-0 and 40-15 down in the second, Melzer broke his racket by smashing it several times on the court. He then won the next four points but finally lost after he double-faulted on Del Potro's second match point.
Del Potro became the fifth Argentine winner of the clay-court tournament in Kitzbuehel in the last six years, after Guillermo Coria (2003), Gaston Gaudio ('05), Agustin Calleri ('06) and Juan Monaco ('07), who withdraw from this year's event with an injury.
Sunday's final of the 63rd edition marked the end of the event, which is not included in the ATP calendar next year.
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Melzer to play del Potro in Austrian Open final
Top seed Seppi withdraws from Austrian Open
