The side currently coached by Rodolfo Cardoso on a temporary basis picked up their first win of the season with Robert Tesche scoring the all-important winner on the road
Martin Harnik's strike in the 18th minute gave the home side the lead yet Hamburg, having sacked coach Michael Oenning earlier this week, leveled the scoring on 51 minutes through Jeffrey Bruma. Robert Tesche's volley in the 67th minute ensured HSV picked up their first win of the season, on their seventh attempt.
The away team, who are being led by Rodolfo Cardoso on an interim basis, move off the bottom of the Bundesliga into 17th place while Stuttgart stay in sixth for the time being.
After a bright opening, Bruno Labbadia's men took the lead in the 18th minute. Zdravko Kuzmanovic's drive from outside the box was parried by Jaroslav Drobny into the path of Harnik who controlled the ball before striking the ball into the net from close range.
However, in the 51st minute, the away side were all square. Gokhan Tore's inviting corner found the head of Chelsea loanee Bruma, who directed his header past Sven Ulreich for his first goal in a HSV shirt.
The coachless club scored what was to be the decisive goal of the game in the 67th minute. Tore's corner was only half cleared by the Stuttgart defence as Tesche slammed his volley on the turn into the bottom corner from 15 yards out, to hand his side an important victory.
Next up for Hamburg is a home encounter against Schalke while Stuttgart travel to Kaiserslautern.