Bruno Labbadia's appointment in midweek failed to provide a spark for Hamburg, who slipped to a club-record sixth successive game without scoring and are without a win since February 7.
There was little to get excited about from Hamburg's perspective at the Weserstadion, with opportunities something of a rarity throughout.
Franco Di Santo scored the game's only goal, converting a penalty kick six minutes from time after Valon Behrami was dismissed for hauling down Zlatko Junuzovic inside the area.
In the day's late kick-off, Wolfsburg needed a late equaliser to salvage a 1-1 draw at home to Schalke, who were denied a first win in five.
Wolfsburg's pressure paid off eventually, however, and it came as little surprise to see Kevin De Bruyne involved, as the Belgian found the bottom corner from the edge of the area with 12 minutes to go.
