Despite a promising start, goals from Aytac Sulu and Jerome Gondorf either side of half-time turned the game in the visitors' favour.
Lewis Holtby grabbed a goal in the dying minutes, though it proved too little too late and they were resigned to a 2-1 defeat.
HSV start well but Sulu punishes profilgacy
Set-pieces provided two excellent, early openings for the hosts in the first 10 minutes. Lewis Holtby swung in a corner to the near post area, which Michael Gregoritsch glanced inches past the far post. Holtby executed a training ground free-kick to perfection moments later, but to see Ivo Ilicevic blaze it over the bar.
Sven Schipplock had another chance but it wasn't third time lucky for HSV, as he couldn't make the most of a well-angled through ball and Christian Mathenia came to Darmstadt's rescue. Konstantin Rausch then tested the home side for the first time, midway through the half, as his free-kick came back off the post, however.
It was Rausch's delivery that would prove crucial later on in the half, when he picked out Sulu. Their inspirational centre-back, who has been one of the league's most impressive players this term, managed to flick into the near post from the edge of the area and suddenly Hamburg's good work was undone.
Holtby's goal comes too late
That goal seemed to have an effect on the hosts' early second-half play, which had a hugely detrimental effect on their defending. Emir Spahic failed to clear the ball twice before letting Sandro Wagner skip past him and into the right-hand channel, where he fizzed in a fantastic ball to Gondorf; he made no mistake to double Darmstadt's lead.
Wagner was proving a handful and sent a header and shot wide of the far post, before Gondorf passed up another chance to add to their tally. However, HSV managed to bring one goal back when Nicolai Müller threaded Holtby through to poke past Mathenia. Darmstadt, unlike so many other times this season, managed to hold on for the win.