Sebastian Langkamp's towering header six minutes from time was enough for Pal Dardai's side to come away from the Imtech Arena with all three points, despite the fact they were on the back foot for much of the game.
Langkamp's intervention came just three minutes after Hamburg defender Cleber Reis saw red for a second bookable offence.
Hamburg dominated proceedings almost from first whistle to last, with captain Rafael van der Vaart twice going close to opening the scoring in the first half.
But Hertha hung in and got their rewards when an unmarked Langkamp directed Marvin Plattenhardt's superb free-kick beyond the helpless Rene Adler.
Victory moves Hertha up to 13th and six points clear of the relegation play-off place, while Hamburg could find themselves as low as second bottom by the end of the weekend, should Paderborn and Freiburg both win on Saturday.
