The hosts' unrelenting pressure told at the end of the first half as Ciro Immobile scored a wonderful individual breakaway goal, before Pierre-Emerick Aubameyang swiftly added a second after half time to put the first three points on the board.
Dortmund were the more dangerous side in the opening period, with Arsenal keeper Wojcech Szczesny having to repel repeated attacks from the hosts. The first opening fell to Aubameyang as the Gabonese striker latched onto Immobile's cross in the six-yard box, but his toe-poked effort was well smothered by the Polish goalkeeper. An even better chance followed a minute later as Immobile again made headway down the left. His cross was palmed out by Szcesny, but Henrikh Mkhitaryan could only fire the rebound over under pressure from Jack Wilshere.
It was then Arsenal's turn to go close, their first meaningful attack leading Kieran Gibbs to float a cross over from the left. Fortunately for the hosts Danny Welbeck couldn't quite get a hold of it and Weidenfeller eventually collected. With the break approaching it looked like Arsenal might have weathered the first-half storm. Immobile, however, had other ideas when he picked up a clearance on the halfway-line and drove at the visitors' defence. His pace took him past Koscielny and his low finish beat Szczesny to lift the roof off the Signal Iduna.
If Arsenal had hoped for a change of fortunes after the break they were to be disappointed, as the hosts doubled their well-deserved lead two minutes into the second half. Kevin Großkreutz dinked a delightful through-ball over the top for Aubameyang and this time he made no mistake, rounding Szczesny and poking the ball home. It was no more than Dortmund's high-octane performance deserved.
Mkhitaryan should have made it three having nicked the ball off Arteta and gone through on goal, but he wastefully fired over. Welbeck was presented the Gunners' best chance late on, but snatched at his shot and cleared the crossbar from the edge of the 18-yard box. From there Dortmund were happy to ease off the pace and see out a comfortable 2-0 win.
Borussia Dortmund: Weidenfeller - Durm, Subotic, Papastathopoulos, Schmelzer (Jojic 79') - Bender, Kehl (Ginter 45') - Aubameyang, Mkhitaryan, Großkreutz - Immobile (Ramos 86')
Arsenal: Szczesny - Bellerin, Mertesacker, Koscielny, Gibbs - Arteta (Podolski 77'), Sanchez, Ramsey (Cazorla 62'), Wilshere, Özil (Oxlade-Chamberlain 62') - Welbeck
Goals: 1-0 Immobile (45'), 2-0 Aubameyang (48')