Jurgen Klopp's team found themselves paired against the Premier League side for a third time in four seasons, having lost 1-0 at Signal Iduna Park last term and shared a 1-1 draw in 2011.
But Arsenal had no answer to waves of furious, pacey attacks from the Bundesliga outfit, who scored either side of half-time through impressive attacking duo Ciro Immobile and Pierre-Emerick Aubameyang.
Italy international Immobile netted his first goal since joined Dortmund from Torino with a superb solo effort, while Aubameyang's display of speed and incision punished Arsene Wenger's men again in the 48th minute.
Tellingly, Arsenal striker Danny Welbeck passed up good chances shortly before both Dortmund goals but the scoreline was ultimately flattering to the England international and his team-mates.
Former Manchester United playmaker Shinji Kagawa started on the bench following a goalscoring return to Dortmund colours against Frieburg on Saturday, while Sven Bender made his first appearance in midfield since February having recovered from a thigh injury.
Arsenal's defensive shortage was well documented before kick-off and, with Calum Chambers only among the substitutes due to a bout of tonsillitis, 19-year-old Hector Bellerin made a debut at right-back.
Mikel Arteta, starting in midfield due to Matthieu Flamini's thigh problem, had an early scare when Henrikh Mkhitaryan went down under his fifth-minute challenge but the Armenian was rightly booked for simulation.
Dortmund enjoyed the better of the opening exchanges but had to wait until the 27th minute for a clear opening, when Arsenal goalkeeper Wojciech Szczesny spread himself to deny Aubameyang on the end of Kevin Grosskreutz's cutback.
Two minutes later Mkhitaryan blazed over under pressure from Jack Wilshere after Szczesny parried a low cross from Immobile.
Sebastian Kehl dispossessed the ineffective Alexis Sanchez and fed Aubameyang, whose tame 34th-minute finish allowed Szczesny to tip wide at the near post.
Welbeck spurned Arsenal's best opening of the half, shooting wide after Aaron Ramsey's deft pass got him in behind the Dortmund defence and the visitors were made to pay on the stroke of the interval.
Immobile stormed forward on the break from his own half and burst between Laurent Koscielny and Kieran Gibbs to arrow a clinical low finish across Szczesny.
Kehl made way for Matthias Ginter at half-time but it did nothing to disturb Dortmund's momentum as they once again tore forward with an intensity Arsenal's defence had no answer to.
Aubameyang forced the Premier League team to backpedal on this occasion and, although he stumbled in rounding Szczesny on the end of Grosskreutz's sumptuous return pass, he managed to steer a bouncing ball past Koscielny on the line.
Szczesny then tipped over a rasping Immobile strike as Dortmund threatened to run riot.
Welbeck could not turn home Gibbs' 57th-minute cross on a rare foray forward, which was was almost punished by Aubameyang - the 25-year-old's electric pace again reducing Arsenal to shreds as he found space to fizz a shot against the top of the crossbar.
Sluggish errors from Szczesny and Arteta were almost capitalised on by Aubameyang and Mkhitaryan as Arsenal's performance threatened to unravel completely.
As the clock ticked down on Wenger's first opening-day loss in the Champions League for 11 seasons, Welbeck turned cutely but blazed over to repeat another theme of the evening.
And the final whistle brought an end to a punishing experience for Arsenal, who will count themselves lucky not to have suffered a heavier loss.
