Son Heung-min and Artjoms Rudnevs decided the encounter in the northern Germany side's favour with a goal in either half of the game, condemning Augsburg to their fifth defeat of the season and leaving them third from the bottom of the table.
It was an unfortunate defeat for the Bavarians, though, as they wasted a hatful of chances on a frustrating night for the fans at the Augsburg Arena.
Augsburg attacked first with Daniel Baier's cross pushed away from the danger zone by Rene Adler with less than a minute on the clock.
The home side were making it immediately clear that they wanted all three points, but the final touch was lacking.
Hamburg were forcefully penned back in their own half, overwhelmed by the Bavarians' attacking play until Rafael van der Vaart saw a way out to set up the opening goal.
His ball forward was not cleared by the Augsburg defence and it fell to Rudnevs, who squared for Son to grab his fifth goal of the season from just outside the penalty area.
Augsburg refused to be disheartened and continued to press and probe, with Stephan Hain just missing the target with a good chance.
The tone of the game did not change at the start of the second half either, with Markus Weinzierl's side throwing everything they had at Hamburg, albeit without any success.
Tobias Werner headed a golden opportunity wide before Baier and Knowledge Musona wasted chances.
A goal was in the air although it came, like in the first half, unexpectedly at the other end of the field in the 63rd minute.
The same trio who were involved in the opening goal combined again, with Son this time starting the move by finding Van der Vaart, who in turn set up Rudnevs to hammer a shot into the roof of the net.
This time, Augsburg's heads understandably dropped. Having controlled the game for an hour, they found themselves with a mountain to climb just to get a point, yet they no longer had the energy to overcome even a foothill as they admitted defeat.