It was the the home side who made the better start to the clash, with Raphael Wolf being forced into making a fine save to keep out Mohamed Gouaida's effort.
Zlatko Junuzovic and Nicolai Muller also squandered decent openings for their respective sides to ensure that it was goalless heading into the interval.
The game remained that way until six minutes from time when Artjoms Rudnevs pounced on a loose ball before firing home to give Hamburg a valuable lead, just moments after Santiago Garcia saw his goalbound header denied by Jaroslav Drobny.
Hopes of a Bremen comeback were made harder in the final minute of normal time when Clemens Fritz was issued a second yellow card, while Wolf conceded an own goal to compound their misery at the death.
The victory lifts Hamburg up to 15th place, one spot and one point clear of Borussia Dortmund, while Bremen drop down to 17th.