Dortmund were much the brighter of the two sides throughout the one-sided match, with Aubameyang and Henrikh Mkhitaryan both spurning excellent chances for the home team early on.
The deadlock was inevitably broken a minute before half-time when Immobile burst past Laurent Koscielny and placed the ball beyond Wojciech Sczcesny to give Dortmund a deserved lead.
The Bundesliga side burst out of the traps in the second half and doubled their advantage when Aubameyang rounded Szczesny and tapped the ball into the net to send the Westfalenstadion into delirium.
Arsenal’s Danny Welbeck had opportunies to score but couldn’t convert his chances, meaning that the Gunners got their Group D campaign off to a dismal start.
Arsene Wenger can at least offer Arsenal’s injury problems as some explanation for their fragility in defence.
Full-backs Nacho Monreal and Mathieu Debuchy were in the treatment room and Calum Chambers was confined to the bench because of tonsillitis, so Spanish teenager Hector Bellerin made his full debut.
Surprisingly, another right-back option Mathieu Flamini was omitted from the squad so Bellerin was given the chance to add to his solitary appearance as a substitute in the Capital One Cup.
The 19-year-old’s first touch would not have calmed the nerves as he needlessly gave the ball away, but it was down Arsenal’s left flank that Dortmund were making the greatest inroads.
Aubameyang and Immobile combined well before a slip by Arteta, who had recovered from his ankle injury to anchor the midfield, left the Gunners exposed.
Once Arteta had recovered, he brought down Mkhitaryan and the Dortmund attacking midfielder was booked for diving by referee Olegario Benquerenca.
Arsenal earned brief reprieves from the constant pressure when Aaron Ramsey and Welbeck tried to unpick the back four and Ozil floated a wonderful long pass to Alexis Sanchez before the flag went up.
Only Szczesny kept Aubameyang at bay after he been released by Kevin Grosskreutz.
It was then the turn of Immobile to maraud free and his final ball was pushed aside by Szczesny, struck Koscielny and fell to Aubameyang, but Ramsey came to the rescue.
The onslaught gathered pace when Sanchez was dispossessed by Sebastian Kehl and this time the side netting foiled Aubameyang.
Sanchez almost reached a long-range free-kick and it was the Chile forward who was carrying the fight to Dortmund on the rare occasions Arsenal attacked.
Remarkably given the one-way traffic, Arsenal should have taken the lead in the 41st minute but Welbeck sent his one-on-one with Weidenfeller wide to beat after the trickery of Ramsey had parted Dortmund’s defence.
On the stroke of half-time Immobile gave a lesson in finishing as picked up possession after a Gunners throw-in, held off Koscielny and crashed the ball past Szczesny.
The result was sealed in the 48th minute when Aubameyang collected a sublime pass by Grosskreutz, rounded Szczesny on the edge of the area and stabbed the ball over the line.
It would have been 3-0 but for Szczesny getting fingertips to a powerful shot from Immobile and Aubameyang hitting the woodwork.
Arteta gave the ball away and Aubameyang should have done better with his ensuing attempt and when Welbeck skied the ball over the crossbar at the other end, Arsenal knew it was not their night.
Alex Oxlade-Chamberlain prevented a near-certain goal with a superb tackle and to complete the Gunners’ misery Jack Wilshere limped off.