The claycourt specialist won 6-4, 6-4 as he followed up last week's win in Vina del Mar, Chile with another title, his first on home soil.
Puerta, a wild card entry who returned to action last year after a serving a nine-month ban for a doping offence, had beaten top seed Carlos Moya on the way to his first ATP final in five years.
"One always dreams about winning in front of your own people," said Gaudio after receiving the trophy from compatriot and former player Guillermo Vilas.
"I've just come from Chile and I've played one game after the other. But, as I was playing in front of the Argentines, I had to make a special effort."
Puerta said: "I'm very happy, I've had a great week. I wanted to win but I was facing a great player who's on the top of his form and you have to play to the limit all the time against him."
Puerta failed to threaten Gaudio's serve in the first set, when a break in the fifth game was enough for the second seed.
The second set was more evenly balanced. Gaudio became increasingly frustrated with the crowd noise and his mistakes while his opponent grew in confidence.
But three unforced errors by Puerta in the ninth game allowed Gaudio to break serve and opened the way for him to clinch the fifth singles title of his career.
