After a first half largely devoid of quality, Ramsey’s goal gave both sides new impetus and Dortmund will feel slightly hard done by not to take anything from the game after probably having the better chances throughout.
Indeed, Arsenal almost went behind in the 17th minute when Neven Subotic volleyed wide after Aaron Ramsey failed to clear a Marco Reus free-kick.
Henrikh Mkhitaryan really should have given Dortmund the lead in the 37th minute having been put through by Jakub Blaszczykowski after the referee waved play on following what looked like a foul on Robert Lewandowski by Laurent Koscielny, but scuffed his shot wide from just inside the penalty area.
Things didn’t improve for Arsenal after the break with Reus failing to find the net with a free header in the 49th minute, before Mkhitaryan fired an effort the resulting corner high over the bar.
Dortmund had the ball in the net moments later, with Reus reacting quickest to a fine save from Wojciech Szczesny following a Blaszczykowski effort, but the goal was ruled out for offside.
Arsenal had rarely threatened in the second period but on a rare foray forward they got the ball into the box where Olivier Giroud cushioned a header back across goal and Ramsey stooped bravely to head past a scrambling Roman Weidenfeller in the 62nd minute.
The game came to life after the opener with Reus missing a chance to equalise and Weidenfeller forced to make a smart save from Ramsey before Nuri Sahin cleared off the line to keep Dortmund in the match.
Arsenal might have had a penalty when Weidenfeller clattered into Koscielny with 11 minutes remaining, but the referee ruled the goalkeeper got to the ball first.
Dortmund threw everything at Arsenal in the closing stages but despite penalty claims from Lewandowski under the challenge of Per Mertesacker, the Gunners held on to secure a valuable away win.
The result sees Arsenal equal on points with Napoli at the top of Group G, after the Italians saw off Marseille.
In other match, Samuel Eto’o scores twice as Chelsea beat Schalke 3-0.
