Aaron Ramsey's second-half header ensured Arsenal picked up three points against Borussia Dortmund at Signal Iduna Park.
The win for Arsenal means the Premier League side remain top of Group F and are now three points ahead of Jurgen Klopp's Dortmund.
Arsene Wenger picked the same starting line-up that defeated Liverpool 2-0 at the weekend, as the Frenchman was desperate for his side to make up for their 2-1 home defeat against Borussia Dortmund at the end of last month.
Borussia Dortmund squandered several opportunities to open the scoring inside the first hour, while Arsenal shot stopper Wojciech Szczesny saved efforts from Marco Reus and Jakub Blaszczykowski.
The Gunners made the Bundesliga side pay for their missed chances by taking the lead through Ramsey.
Arsenal's in-form midfielder scored his 11th goal of the season by heading home a Mesut Ozil cross in the 62nd minute.
Dortmund went in search of an equaliser, however last season's Champions League runners-up were unable to break down Wenger's side as Arsenal hung on to secure a famous win.