Robredo, who lives in Barcelona, defeated Gaudio 6-3, 4-6, 6-2, 3-6, 6-3 in a match that lasted 3 hours, 46 minutes.
"Winning at home is very important to me," said Robredo, 22. "My childhood dream has come true. It was a very tough match, and I'm happy that I won."
Robredo was the 11th Spaniard to win the claycourt tournament. Gaudio won the event in 2002.