Hannover had put together an impressive pre-season campaign, which included victories over Rangers and Real Madrid, but they struggled against a stubborn Hamburg defence.
Neither team created many chances in the first 20 minutes, but Hamburg grabbed the lead when Benjamin fired home a fierce volley in the 23rd minute.
Piotr Trochowski started the move that led to the goal, finding Nigel de Jong in space on the left.
He then chested down to Benjamin to fire a fine right-footed effort into the top right-hand corner.
Hamburg nearly went 2-0 up in the 35th minute but Hannover goalkeeper Robert Enke was able to beat away Mohamed Zidan's shot after a mazy solo run.
Hannover's first real chance came on the hour mark, Vahid Hashemian's shot from in front of the goal fizzing just over the cross bar.
Two minutes later, Hamburg keeper Frank Rost had to palm away Szabolcs Huszti rising effort.
Hamburg then hit back, pushing forward to create the opening for Trochowski to fire a long-range effort against the crossbar on 70 minutes, while Enke kept out Guy Demel's lofted header a minute later.
And Hannover was again saved by the crossbar when Rafael van der Vaart slammed against the woodwork 10 minutes from time.