The hosts went ahead through Alfred Finnbogason, only to be pegged back in the latter stages of the first half by Michael Gregoritsch.
Nicolai Müller struck just after the hour mark to give HSV the lead, with Gregoritsch grabbing his second to round off the scoring.
Level at the break
Before the game Finnbogason and Jeffrey Gouweleeuw announced extensions until 2020, as well as Markus Feulner for another season, the former fired Augsburg into an early lead. A mix-up between Tom Mickel and Johan Djourou let the Icelandic forward score his seventh goal in 14 Bundesliga games.
Augsburg continued to come forward with Mickel responding well to the early mishap and denying strong efforts from Halil Altintop and Caiuby in quick succession. Then, surprisingly, it was HSV who would score next. Müller was fouled by Christoph Janker and Gregoritsch stepped up to send the ball straight into the top corner; stunning strike.
Jeong-Ho Hong came to the hosts' rescue just before the interval as he hacked Müller's chip off the line.
HSV push on to secure three points
Aside from a Philipp Max effort, which Mickel did well to parry, Augsburg were not in the game after the break. Marwin Hitz did well to deny Pierre-Michel Lasogga but he was unable to prevent Müller from putting his side ahead. After Gregoritsch had flicked on Nabil Bahoui's corner, and the winger was able to finish from close range.
It was a similar story for Gregoritsch's second goal, as Cleber's header was blocked by Daniel Baier but fell kindly to the Austrian. The former Bochum winger has taken to the Bundesliga like a duck to water, and tapped in from three yards out to seal the points. HSV ended the season in a respectable 10th, with Augsburg coming in at 12th.