Struggling pair Nuremberg and Augsburg were involved in a goalless draw in the other match, a result which kept both sides firmly entrenched near the bottom.
Nuremberg, who at least ended a run of four successive defeats, are 15th with eight points while Augsburg are 16th with six.
After a terrible start to the season, Hamburg had taken 10 points from their previous four games but that run was ended by Vedad Ibisevic's goal after half an hour.
The Bosnia forward beat his marker to Martin Harnik's low cross from the right and turned the ball past goalkeeper Rene Adler to break the deadlock with his fourth goal of the season.
Hamburg are 10th with 10 points from eight games, one ahead of Stuttgart who are one point and two places below.
Bayern Munich, who won 5-0 at Fortuna Duesseldorf on Saturday, lead with a maximum 24 points from eight games, five clear of Eintracht Frankfurt.
- Vedad Ibisevic