Gilberto Silva's 12th minute penalty handed Arsene Wenger's side the initiative at the AOL Arena, but it was the dismissal of goalkeeper Sascha Kirschstein in the build-up to the goal that cost Hamburg dear on the night.
Silva, who was handed the captain's armband after Thierry Henry was forced to sit out the clash with a recurrence of a foot injury, confidently drilled the spot-kick beyond substitute keeper Stefan Wachter whose first task was to pick the ball out of the back of the net.
Kirschstein had seen red for clipping the heels of the lively Robin van Persie who found himself one-on-one with the keeper after some intelligent play by Emmanuel Adebayor.
The contact was enough to send the Dutchman falling to the ground and, after Silva stroked home the resulting penalty, there was no way back for the home side.
Van Persie could have secured the three points in the first half but he twice pulled angled shots across the face of goal and was flagged marginally offside in the process.
Arsenal lost influential defender Kolo Toure midway through the first half with a back injury and it almost proved costly as highly-rated Belgian youngster Vincent Kompany came within a whisker of heading Hamburg level from a near-post corner soon after his withdrawal.
But Arsenal's dominance on the ball was rewarded eight minutes into the second half when Tomas Rosicky scored his first goal since a £7million summer switch from Borussia Dortmund.
The Czech Republic international was given time and space 25 yards from goal to size up and execute a looping shot over the despairing keeper and into the top left-hand corner of the net.
If the strike came out of the blue then the result was certainly anything but after that moment of magic and, with half an eye on Sunday's Premiership clash with Manchester United, the Gunners rang the changes with Aleksandr Hleb and van Persie replaced by Julio Baptista and Mathieu Flamini on 70 minutes.
Silva should have doubled his tally on the night in the 76th minute but the Brazilian headed a Flamini corner over the bar from six yards when left totally unmarked.
To Hamburg's credit they continued probing right to the final whistle and Boubacar Sanogo saw a late effort ruled out for offside after Piotr Trochowski's shot had clattered against the crossbar.
But the Hamburg striker did get his name on the scoresheet in stoppage time when he had the simple task of scooping the ball into the unguarded net after David Jarolim took Jens Lehmann out of the equation with a neat cut-back.
However, it was little more than a consolation strike for Hamburg who were well-beaten on the night despite the scoreline suggesting otherwise.