The Gunners are safely through to the knockout stages of the competition after a brace by the Dutchman as he continues his impressive goal form.
Arsenal found themselves on the back foot in the first half, failing to create any real opportunities. However, a double from Robin Van Persie saw the Gunners qualify with a match to spare and win Group F.
Both Arsenal and Dortmund named unchanged teams from their weekend victories to Norwich City and Bayern Munich respectively.
The in-form trio: Theo Walcott, Robin Van Persie and Gervinho spearheaded the attack for the Gunners while 19-year-old Mario Gotze and star striker Robert Lewandowski were both given the nod.
Dortmund appeared the hungrier of the two sides from kick-off. The German outfit almost created an opening in the first minute: Gotze slipped an intelligent pass to Lewandowski but Wojiech Sczcesny came out quickly to collect the ball in his box.
Just as the game began to quieting down on 20 minutes, Aaron Ramsey chipped a scintillating pass to Walcott, who had his attempt blocked by keeper Roman Weidenfeller who came charging out.
Around the half-hour,Jurgen Klopp’s side then faced two significant setbacks in quick succession. Sven Bender was carried off on a stretcher following a collision with Thomas Vermaelen which resulted in midfielder lying prone and needing attention to his head.
While Gotze came off after failing to recover from a knock he picked up earlier on in the match. Moritz Leitner and Ivan Perisic were the two substitutions utilised.
On the 44th minute Walcott almost provided the ingenuity to unlock the Dortmund defense. After dummying and allowing the ball to roll to Ramsey, Walcott received the ball back and crossed a sumptuous low ball from the right flank, but Weidenfeller got a fist to the ball to divert it away.
After a disappointing first half from the home side, Arsenal began the second half with the dynamism expected from a team eager to secure qualification.
But it was the German charges who created the first promising chance after the whistle: Shinji Kagawa and Lewandowski exchanged passes on the edge of the box before Kagawa has his shot blocked by Szczesny from a tight angle.
However, it was Arsenal who proved clinical with their first real opportunity of the half. On the 49th minute, the effervescent Van Persie continued his excellent goal scoring form with the opener of the game.
Alex Song showed great skill on the left flank, tricking his way past three Dortmund defenders and crossing a perfect ball to Van Persie who headed into the bottom right.
Minutes later, the Gunners squandered the opportunity to extend their lead. Ramsey poked a through-ball to Gervinho who found himself free in front of goal with only the keeper to beat, however the Ivorian, looking to take the ball past the keeper, was tackled by Mats Hummels in the process.
Yossi Benayoun later replaced Gervinho with half an hour to play in a tactical change by Arsene Wenger to see out the game.
Arsenal’s work rate allowed them to dominant large portions the second half with Ramsey and Song permeating the midfield, as Dortmund struggled to get back into the game
Arsenal's talisman, Van Persie, wrapped up victory for the home team on the 86th minute after an Arteta corner was flicked on by Thomas Vermaelen for the Dutchman to smash the ball home from two yards.
The Gunners looked as if they would finish the game with comfort but a last minute goal from Kagawa made for a nervous final minute. Lewandowski recieved a ball from a corner and fed the ball to the midfielder who finished from close range. However, the goal was too late as Dortmund exited the competition.