كتب : Hatem Maher
Peru striker Jose Paolo Guerrero gave Hamburg the lead after 19 minutes with a close-range shot.
He scored his second of the night six minutes past the hour mark to double the hosts' advantage.
Cologne's Moroccan substitute Adil Chihi narrowed the gap on 76 minutes after his powerful long-range shot left the keeper with no chance.
A penalty from Piotr Trochowski four minutes from time made sure of Hamburg's victory that put them on top with ten points from four games, ahead of second-placed Bayer Leverkusen on goal difference.