The Gunners failed to have a single shot in the first half, and the closest they came to a breakthrough was when Olivier Giroud tried to burst through the Dortmund defence, only to be pulled back for handling the ball.
At times Arsenal struggled to deal with the pace and control of Dortmund. Mikel Arteta was booked for pulling back Jakub Blaszczykowski on the 24th minute. He was lucky to escape a second yellow for a tackle from behind on Robert Lewandowski.
The best chance for Dortmund came on 37 minutes as Lewandowski broke down the right hand side, Blaszczykowski picked up the ball and squared it to Henrikh Mkhitaryan, only to see him curl a shot just wide. Neven Subotic also went close when his volley dribbled past the post.
Just after the hour, out of nowhere, Arsenal took the lead. Mesut Ozil stood up a cross to the back post for Giroud, who won the ball, sending it up across goal. Aaron Ramsey was quick and brave, ahead of the defence to put the ball past Roman Weidenfeller.
Following the goal, Arsenal grew into the game, and came close through Per Mertesacker, a Ramsey volley and a Sokratis Papasathopouos tackle. While Dortmund responded with sustained periods of pressure, they couldn’t find a breakthrough.
17' - SUBOTIC CHANCE - Reus heads on a corner, but Subotic's hooked volley dribbles past the post.
37' - MKHITARYAN CHANCE - Błaszczykowski lays the ball square for Mkhitaryan but the Armenian sends his curling shot just wide.
50' - REUS CHANCE - The ball is crossed to the back post and Reus' powerful header is saved brilliantly by Szczesny.
62' - RAMSEY GOAL - Ozil's cross from the right is headed upwards by Giroud, and Ramsey is first to it as it drops, heading it past Weidenfeller to put Arsenal ahead.
64' - REUS CHANCE - Lewandowski sends in a low cross in the six yard box but Reus totally fails to connect.
65' - RAMSEY CHANCE - This time Giroud sends the ball in, Ramsey chests down and blasts it at the keeper.
70 - MERTESACKER CHANCE - Mertesacker heads just over the post after flicking on a deep free kick.
Arsenal have scored in their last nine Champions League games in Germany.
Arsenal did not have a single shot in the first half.
This is Arsenal's first victory at Dortmund.
TALKING POINT: Will Arsenal get even better? With Mathieu Flamini to come back from injury, and possible reinforcements to come in January, there is no reason why Arsenal cannot sustain this performance level well into the rest of the season.
MAN OF THE MATCH: Per Mertesacker (Arsenal): Mertesacker was solid and calming in defence throughout, and was close to extending Arsenal's lead with his threat at set pieces.
Borussia Dortmund: Weidenfeller 6, Subotic 6, Papastathopoulos 6, Schmelzer 6, Bender 6, Reus 6, Błaszczykowski 6, Nuri Sahin 5, Grosskreutz 7, Lewandowski 6, Mkhitaryan 6. SUBS: Hofmann 6, Aubameyang 5, Schieber 6.
Arsenal: Szczesny 7, Sagna 6, Mertesacker 8, Koscielny 6, Gibbs 7, Rosicky 6, Arteta 7, Ozil 6, Ramsey 7, Santi Cazorla 6, Giroud 7. SUBS: Vermaelen 6, Monreal 6, Bendtner 6.
MATCH IN A TWEET