Igor de Camargo headed home the game's only goal in the 66th minute to send Lucien Favre's side level on 13 points with Werder Bremen at the summit, although Bayern Munich can regain top spot tomorrow with victory at Schalke.
The result was a fourth win in six games this term for Monchengladbach, who only avoided relegation last season courtesy of their play-off victory over Bochum, while for HSV it was a fifth defeat.
The struggling hosts had the early initiative but could not create any clear openings.
David Jarolim burst clear on the counter-attack only to be let down by a heavy touch in the sixth minute, and 15 minutes later Tomas Rincon lashed just wide of Marc-Andre ter Stegen's right post.
Marco Reus passed up Gladbach's best chance of the half when he fired over in the 28th minute, but the visitors were for the most part of the opening 45 minutes kept at bay by the outstanding Slobodan Rajkovic .
Gladbach came out for the second half seemingly intent to find the breakthrough and sounded a warning in the 48th minute, Reus playing a neat one-two with De Camargo before arrowing his shot towards the bottom corner only for Hamburg goalkeeper Jaroslav Drobny to make a fine save with his feet.
Hamburg could have gone ahead themselves just before the hour when Robert Tesche's header was cleared off the line by defender Filip Daems, but midway through the second half they were behind.
De Camargo did well to beat Rajkovic to Juan Arango's free-kick, and his downward header gave Drobny no chance.
It could have got even worse for Michael Oenning's side in the final quarter as Gladbach grew in confidence and could have added to their lead.
Reus was unable to beat Drobny from a tight angle and the HSV stopper then did brilliantly to parry an Arango blast following good work down the left by Reus, but Gladbach already had the points in the bag.