Potro, who turned 18 on Saturday, dispatched the former French Open champion in just over an hour for what was easily the biggest victory of his career.
Moya, ranked 43rd in the world, is a favourite in India where he has won the Chennai Open twice and finished runner-up to Croatian Ivan Ljubicic in January.
But he made too many errors as the 1.95-metre Potro, ranked 106 in the world, pounded him with big serves and powerful strokes.
"It's a very big win as he is a big-calibre player and one of my heroes," Potro told reporters through an interpreter.
"Obviously it gives me a lot of confidence to go on in the tournament.
"I played on his backhand because he likes to move around on his forehand," said Potro, who added that he was playing his first Tour event on hard court. All his previous tournaments were on clay.
"I had an off day," said Moya. "I was just not hitting well."
"He hits the ball very hard. I think he has a bright future."
Stefan Koubek of Austria beat seventh seeded Argentine Juan Monaco 7-6 6-4 in the day's other upset. Eighth seed Wesley Moodie of South Africa downed Indian wildcard Rohan Bopanna 3-6 7-6 6-4.