Federer won 4-6, 6-4, 6-2, 6-3 over the Argentine. It was Federer's second Hamburg title and 15th of his career. He has won four tournaments this year, including the Australian Open, the first of the Grand Slams.
The world's No. 1-ranked player said he's looking forward to the French Open, which begins May 24, saying he's a more relaxed player now and knows "how to approach Grand Slams."
Coria had won 31 straight claycourt matches until his loss to Federer.
"The difference was that Federer was physically on a higher level," Coria said. "That's what made him win the match.