The northern club, who were on the brink of relegation three times in the last four seasons, made it two wins out of two league matches thanks to first half goals from newcomer Andre Hahn and American Bobby Wood and a late one from Lewis Holtby.
Hamburg scored against the run of play when Hahn whipped in his first ever shot for his new team after Cologne had failed to clear a corner in the 28th minute.
Some more sloppy Cologne defending six minutes later allowed Wood to slip into the box and double their lead.
Cologne twice hit the woodwork either side of the break with Jonas Hector and Jhon Cordoba but their momentum was disrupted when referee Felix Brych went off injured, forcing a 10-minute break for his replacement, Soeren Storks, to get ready.
Hamburg were then left with 10 men when Mergim Mavraj was sent off with a second booking and Cordoba had another huge chance but Hamburg keeper Christian Mathenia's superb point-blank double save protected their two-goal cushion.
In a frantic finale Frederik Soerensen got a deserved goal for the hosts but substitute Holtby restored the visitors' advantaged three minutes later killing off Cologne's hopes of a comeback.
There was another record for Hamburg as Dennis Diekmeier became the first Bundesliga in-field player to have gone 183 matches without having scored a goal.
Champions Bayern Munich can also make it two wins in a row when they travel to Werder Bremen on Saturday while Borussia Dortmund, who also won their season opener last week, host Hertha Berlin.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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