The Spaniard won the opening set in only 18 minutes, losing just six points with Fognini helpless to reverse the rout from the clay-court baseline.
Fognini broke Robredo twice in the second set but could only hold serve once himself.
"No money can buy this feeling," Robredo said. "I played a perfect match, did a great job. But in matches like this it is always important to win."
Robredo also won on clay at the Grand Prix Hassan II in April in Casablanca, Morocco. Eleven of his 12 titles have been on the surface.
The result halted an impressive run by Fognini. The Italian captured two titles in winning 13 straight matches en route to the Umag final. He won both tournaments in Germany, in Stuttgart two weeks ago and Hamburg last Sunday.
"Probably too many matches behind me - and no match tonight," Fognini said. "I had no power, he deserved to win. I am disappointed but I played three incredible weeks. It will stay in my memory my whole life."
In the 24-year history of the Croatia Open, a Spaniard has won 10 times. Former No. 1 Carlos Moya holds the record with five victories.