Despite investing significantly following their narrow escape from relegation last season, Hamburg have started the new campaign wretchedly.
A 0-0 draw at newly-promoted Cologne on the opening weekend was swiftly followed up by an embarrassing 3-0 home defeat to Paderborn, the other Bundesliga newcomers.
Mirko Slomka's men did show some promise on Sunday, but Hannover were ultimately worthy of their victory at the HDI Arena.
Hannover broke the deadlock with just 13 minutes on the clock, Leon Andreasen heading past Jaroslav Drobny in the Hamburg goal following an excellent cross from Miiko Albornoz.
The visitors had seven new signings involved from the start, including Valon Behrami, Nicolai Muller and Lewis Holtby.
However, Hannover went on to double their lead in the 24th minute as Artur Sobiech netted from close range, bundling over the line after initially firing at Drobny.
Muller went close in the second half, but Hamburg were unable to find a reply.
Sunday's other match saw Eintracht Frankfurt fail to move level on seven points with Bayern Munich and Bayer Leverkusen at the top of the fledgling table, as they lost 1-0 at home to Augsburg.
Following defeats to Hoffenheim and Borussia Dortmund, Augsburg were not to be denied a win at the third time of asking.
Frankfurt goalkeeper Kevin Trapp made a number of saves in the first half, but failed to prevent Augsburg moving ahead in the 49th minute.
Raul Bobadilla pounced on a loose ball in the area after Halil Altintop had been dispossessed and fired a precise finish in off the left-hand post, which proved the only goal of the game.