Artjoms Rudnevs' well-struck volley early in the second half was the only goal of a hotly contested encounter, which ultimately produced few clear-cut chances.
The hosts began the match looking every bit the side with the worst Bundesliga record since the turn of the year, having picked up just four points from seven games. Low on confidence in the wake of a 2-0 home defeat to S.S. Lazio in the UEFA Europa League on Thursday, Stuttgart's strategy appeared to be designed merely to keep Hamburg as far away from their penalty area as possible.
The hosts midfield was initially bypassed as long punts forward brought them the desired security, although the guests' defence, marshalled by the oak-like Heiko Westermann and Jeffrey Bruma, had little trouble repelling their advances. HSV were far more intricate going forward, but with South Korean attacker Heung Min Son given a rest, a vital component was missing as the visitors also struggled creatively.
It was perhaps inevitable then that a set-piece brought the first ripple of approval from the Mercedes-Benz Arena crowd. Raphael Holzhauser's 25-yard free-kick took a deflection off the wall on its way goalwards, forcing Hamburg custodian Rene Adler into a rapid sideways shuffle to divert the ball onto the crossbar. It proved to be the only real sniff of goal either side would have in an intensely-fought first half.
Both teams re-emerged from the changing rooms determined to change the status quo. Stuttgart went closest first, when Serdar Tasci's close-range header from a corner brought a superb reflex save out of Adler, before Rudnevs broke the deadlock in spectacular style at the other end for his eleventh goal this term. Dennis Diekmeier's deep cross from the right found the Latvian 15 yards from goal and the striker's volley on the swivel proved too powerful for Sven Ulreich to handle.
It was the eleventh time this season that Stuttgart had gone behind and perhaps aware that they had previously lost seven of those matches, the hosts began to look deflated. By way of contrast Hamburg became ever more composed, with Norwegian international Per Skjelbred pulling the strings in midfield.
However, wary of committing too many men forward and leaving themselves exposed, the guests eased off in the closing stages and sought instead to control possession. To their credit, Stuttgart kept pounding away but their efforts were too predictable to cause Hamburg any real concern, allowing the guests to move into the top six for only the third time this season and leaving the sinking Swabians just eight points above the relegation zone.
Line-ups and statistics