The summer signing was on fine form as last season's runners-up made an impressive start to the 2013-14 league campaign
Summer signing Pierre-Emerick Aubameyang grabbed a hat-trick and was a constant threat at the SGL Arena, becoming the sixth player in Bundesliga history to net a treble on his debut.
A Robert Lewandowski penalty with just five minutes remaining capped the rout for the visitors.
Augsburg put in a workmanlike performance but failed to trouble the Dortmund defence on many occasions.
After a tepid opening, Aubameyang opened Dortmund's account for the season with a diving header. He followed that up in the second half with a low drive from a Reus throughball, before rounding the goalkeeper for his third.
Juergen Klopp was without goalkeeper Roman Weidenfeller through suspension, with Mitchell Langerak coming in, while full-back Lukasz Piszczek and new signing Henrikh Mkhitaryan missed out through injury.
Augsburg had trouble of their own in the goalkeeping department with Mohamed Amsif deputising for the injured Alex Manninger, while Halil Altintop made his debut up front.
The away side almost made the perfect start in the opening minute when a Kevin Grosskreutz long ball ricocheted into the path of Aubameyang. He broke down the right and played the ball into the path of Lewandowski but the Pole’s effort was blocked by Jan-Ingwer Callsen-Bracker.
But Markus Weinzierl's side were not overawed and pressed their opponents high up the pitch, going close through Altintop’s first-time volley, although it went wide of goal.
The Bavarian side's gutsy plan came undone, however, as the visitors broke the deadlock in the 24th minute.
Marcel Schmelzer received the ball on the left-hand side of the pitch before delivering an exquisite lofted cross straight into the six-yard box where Aubameyang stole away from his marker to finish with a low diving header.
That goal re-energised a lacklustre Dortmund with Reus and Lewandowski becoming more involved further up the pitch.
Raphael Holzhauser went close twice shortly before the break as an effort was cleared off the line before Langerak strongly palmed away the Austrian’s 30-yard effort.
Dortmund almost doubled their lead five minutes after the restart. Holzhauser's pass was intercepted and the away side launched a swift counter-attack.
The ball was moved to Aubameyang on the right where the Gabon international strode into the box and fired an effort towards the near post and was only denied by a good save from Amsif.
But he was not to be denied in the 67th minute.
Reus took ownership of the ball in the middle of the opposition half and slid a well-timed through-ball into the path of Aubameyang on the left-hand side of the box and the new-boy coolly slotted his effort across the goalkeeper into the far corner.
It got better for the forward with 10 minutes remaining. He sprung the offside trap to latch onto a Lewandowski through-ball before rounding Amsif and firing into the empty net.
There was time for one more as Jonas Hofmann was fouled in the box by Kevin Vogt. Lewandowski powered his effort beyond Amsif to open his account for the season and complete a comfortable opening-day victory for Dortmund.