Piotr Trochowski's (69.25 points FTBL reiting) free-kick inside the final 20 minutes secured the points for Hamburg to leave Gladbach still waiting for a first home win of the season.
Gladbach duo Igor de Camargo and Marco Reus were denied by Hamburg keeper Frank Rost in the opening 10 minutes, while Michael Bradley also had a shot saved.
Rost almost gifted the hosts the opener after 26 minutes when he came out of his area to clear but only found Juan Arango, but he was let off the hook when the Venezuela midfielder's 40-yard attempt drifted just wide.
The deadlock was broken by the visitors moments after the interval, when Eljero Elia latched onto a neat back-heel from Jonathan Pitroipa and fired low past Christofer Heimeroth.
The hosts were back on level terms just 74 seconds later, however, when the influential Bradley weaved his way to the byline and floated a perfect left-footed cross into the middle for De Camargo to nod in a simple finish.
Gladbach should have gone ahead in the 70th minute when United States midfielder Bradley brilliantly played in Thorben Marx, but Rost came out and made himself big to block the shot.
And the Bundesliga basement boys were soon made to pay for that miss as HSV scored the decisive goal just two minutes later.
Seemingly distracted by the near-post run of Paolo Guerrero, Heimeroth misjudged the flight of Trochowski's free-kick from the left and could not prevent it going past him seemingly without a touch from an attacker.
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