Aaron Ramsey’s goal makes the Gunners the first English side to win at the Signal Iduna Park, keeping them top of Group F in the process.
The visitors took the lead in the 62nd minute with a header from Aaron Ramsey – the side’s first attempt on goal – and went on to repel a late siege from Dortmund to secure a valuable three points.
Victory leaves Arsenal top of the group on nine points, while Dortmund – playing their 100th tie in the European Cup – slip out of the top two as a result of Napoli’s win over basement club Marseille.
Jurgen Klopp made one enforced change from the side that stormed to a 6-1 Bundesliga victory over Stuttgart on Friday, with Mats Hummels (thigh) making way for Neven Subotic.
Arsenal, meanwhile, were unchanged from a 2-0 victory over Liverpool that sent them five points clear at the top of the Premier League.
The result of the other games is stated below;
Basel 1 – 1 Steaua Bucuresti
Chelsea 3 – 0 Schalke 04
Borussia Dortmund 0 – 1 Arsenal
SSC Napoli 3 – 2 Marseille
Zenit Petersburg 1 – 1 FC Porto
Atletico Madrid 4 – 0 Austria Wien
Ajax 1 – 0 Celtic
Barcelona 3 – 1 AC Milan