The Gunners did not have a shot in a first half that Dortmund should have taken the lead in when Henrikh Mkhitaryan missed a really good chance from just inside the box.
As the pressure built on Arsenal's goal Aaron Ramsey netted once again and his side were able to hold on for what could be a priceless win.
Here, Sports Mole analyses the result.
On target 4
On target 2
Was the result fair?
It has to be a no. Although Arsenal defended admirably, in particular the first half, they did not deserve to take the three points. If their defeat last time to Dortmund was harsh, then this was even more so for the Germans. The goal came against the run of play and after two disallowed goals – rightly – for the hosts. They will be delighted, of course.
It was not as good as everyone had come to expect from Jurgen Klopp's side, but having said that they still did enough to win the game. Their response to being shut out in the first half was excellent and they were really starting to turn the screw before the hammer blow. In all, the fact that they struggled to break down Arsenal suggests that – however well the Gunners defended – they should have done better.
Defensively, they were brilliant. In the first half Dortmund were restricted to largely half-chances, although Mkhitaryan should have scored. They defended from the front and did an awful lot of running. Going forward they had to be patient and they really did take their chance when it arrived. Arsene Wenger will be delighted that his side showed that they were effective at the back as well as going forward.
Sports Mole's man of the match
Tomas Rosicky: Although the Gunners did not have a lot of joy going forward, Rosicky was always their most creative player. He was all over the midfield and rightly got a big reception from the travelling fans when he was taken off.
There were not many mistakes at all in the game, with both sides keen not to give anything away. This has to go to Mkhitaryan for a glaring miss in the first half. He was clean through and sliced his shot wide with only Wojciech Szczesny to beat.
Bjorn Kuipers did very well in what were difficult conditions in front of a loud Dortmund crowd. He had a couple of penalty calls to make – one each way – but refused to be bullied by the players. Overall, he let the game flow and only went to his pocket when needed. A good showing.
Dortmund: It is a return to league action for tonight's hosts and they face a tricky away encounter at Wolfsburg as they look to keep up with Bayern Munich at the top.
Arsenal: Arsenal, five points clear in the league, face a huge clash away to Manchester United at the weekend in what is a real test for Wenger's men.