Robert Lewandowski was also among the goals, scoring a penalty lane on.
Augsburg fought hard to keep themselves in the game for almost 70 minutes, but tired towards the end of the match.
Read how all the action unfolded below:
2.01pmGood afternoon. Last season's Bundesliga runners-up get their new season underway in around half an hour at Augsburg. Let's take a look at the team news.
2.03pmAUGSBURG STARTING XI: Amsif, Verhaegh, Klavan, Altintop, Holzhauser, Baier, Moravek, Callse-Bracker, Ostrzolek, Hahn, Molders
2.05pmBORUSSIA DORTMUND STARTING XI: Grosskreutz, Subotic, Hummels, Schmelzer, Bender, Sahin, Aubameyang, Gundogan, Reus, Lewandowski
2.08pmThe big news for Dortmund is that Pierre-Emerick Aubameyang will make his Bundesliga debut this afternoon as he's preferred to Jakub Blaszczykowski. The 24-year-old is the first footballer from Gabon to play professional football in Germany.
2.10pmTurkish international Halil Alintop makes his debut for the home side this afternoon. The 30-year-old joined Augsburg from Trabzonspor earlier this summer.
2.13pmLast season, Jurgen Klopp's side recorded two comfortable wins over Augsburg, beating them 3-1 at the SGL Arena, before securing a 4-2 victory at home. Dortmund will be hoping for a similar scoreline again this afternoon in order to keep pace with Bayern Munich, following their 3-1 win over Borussia Monchengladback yesterday evening.
2.17pmDortmund got off to a winning start in the DFB Pokal last week. Ahead of this afternoon's match, on-loan midfielder Nuri Sahin told the league's official website: "We moved the ball around pretty well. We could have maybe injected a bit more pace into the match, but then Wilhelmshaven were playing very deep. That doesn't make it any easier for us deeper-lying midfielders to pick out the gaps. From here on we're settling into the normal Bundesliga rhythm. The win at Wilhelmshaven was a successful start, which is all that matters."
2.21pmAugsburg are expecting to be involved in the league's relegation battle again this season, having narrowly secured their Bundesliga status in the last campaign. Sporting director Stefan Reuter recently admitted: "All we're thinking about is avoiding relegation."
2.25pmUnderstandably, Dortmund are heavily favoured by the bookmakers for this afternoon's match, and it's difficult to argue against them to be honest. They may have lost Mario Gotze during the summer, but many of the other key players that helped them reach the Champions League final last season remain. I could see Dortmund winning this 3-0 or 4-0 this afternoon.
2.28pmThe players are just getting ready to leave their dressing rooms and head out to the pitch to get their Bundesliga seasons underway. Jurgen Klopp looks calm and composed as he gathers his team together, while there are some slightly more nervous expressions on the Augsburg players' faces.
2.30pmAnd the players do indeed head out of the tunnel and get into position ready for kickoff, which should be just moments away.
0 minDortmund get the first half underway.
2 minCHANCES! A defensive mix-up from Augsburg gives Pierre-Emerick Aubameyang a chance to break into to box. He pulls it back to Lewandowski, but the Polish striker's finish is deflected wide for a corner. The home side clear the danger quickly, allowing Hahn to go on the counter for Augsburg, but Langerak was able to comfortable block his shot. A lively start by both sides.
6 minAfter the frantic opening couple of minutes, both sides have settled a little, with the visitors dominating possession. A long ball forward finds Reus on the edge of the box, but the delivery has too much pace for the midfielder to control, and it rolls harmlessly to Amsif.
9 minBorussia win a free kick around 35 yards out. On-loan midfielder Nuri Sahin blasts the ball into the penalty area, where Mats Hummels was waiting, but his header was comfortably saved. Dortmund have quickly won the ball back though, and threatening again.
11 minFollowing a rare spell of possession inside the Dortmund half, Moravek tries to break into the box for Augsburg, but Subotic is on hand to take the ball away and tap it back to Langerak. Augsburg appear to be growing in confidence though.
14 minHahn whips in a cross right in front of the Dortmund goal, but Langerak manages to take it before any of Hahn's teammates can reach the ball. The Australian keeper has probably been kept a little busier than he would have expected. Augsburg are really finding their feet now.
17 minSubotic has to be alert again as Molders climbs high to control a long ball forward on the edge of the penalty area. The centre back wins the ball and Dortmund immediately apply pressure at the other end of the pitch, winning a corner. Subotic and Hummels both move forward, but Hummels' header fails to find the target.
19 minCHANCE! Molders has the ball again and looks to get a shot away for the hosts, but he is covered by a pair of Dortmund defenders. The striker tries to keep the threat alive, attempting to pull it back to Hahn, but Subotic manages to clear.
22 minDortmund looked in complete control for much of the opening 10 minutes, but Augsburg have fought their way back in, and look the more likely of the two sides to break the deadlock at the moment. After a high-paced spell, the home side have just slowed the play down a little, but are keeping the ball well in midfield.
24 minGOAL! Augsburg 0-1 Borussia Dortmund (Aubameyang)
26 minPierre-Emerick Aubameyang marks his Bundesliga debut with a fantastic goal for Borussia Dortmund. Another defensive mistake by Augsburg allows the Gabon international through for a one-on-on with Amsif, and he heads the ball low leaving the keeper no change. That will have settled a few nerves among the Dortmund camp.
30 minWell that's changed the game a bit. Straight away, Dortmund look for a second, with Lewandowski looking to get involved. The Pole has been kept relatively quiet so far this afternoon. Klopp had began to show some frustration just before the goal, having words with the fourth official, but Aubameyang's finish appears to have calmed him down.
33 minPENALTY APPEAL! Altintop wins the ball in midfield for Augsburg before finding Hahn out wide. The ball is knocked out of play by Reus, and Hahn almost finds Molders with a long thrown in, but the striker is bundled to the ground. He and his teammates instantly appeal for a penalty, but the referee instructs them to play on. The crowd are not impressed with the officials.
35 minLooking back at the replay of the Molders penalty appeal, he does tangle with Grosskreutz, but it looks more like he loses his footing than a foul. On this occasion, it looks like it was a good decision by the referee.
38 minThe crowd are livid as Reus and Moravek tangle in midfield, resulting in a free kick for the visiting side. Reus takes it, but his delivery is too long, missing all of his teammates on the edge of the penalty area and flying straight into the hands of Amsif.
40 minDaniel Baier is injured as he and Sahin both jump for a high ball in midfield. After a few moments, the midfielder seems to be ok, and the home side try to press forward from the free kick, but Bender is able to regain possession for Dortmund before Augsburg get too close to the visitors' goal.
41 minCHANCE! Grosskreutz feeds the ball through to Reus just to the right of the goal. The midfielder has plenty of space, but takes too long to get his shot away, and finds himself under pressure as Augsburg get numbers back, and the chance is gone.
43 minCHANCE! Augsburg win a corner and Bender has to clear off the line as Klavan tries to head in from close range. The home side get another corner, but its quickly dealt with by Dortmund.
45 minCHANCE! Holzhauser tries to drill in a long-range effort, which almost deceived Langerak as it weaved through the Dortmund defenders, but the Australian spotted it at the last moment, and managed to palm it away while diving to his left.
45 minHALF TIME: Augsburg 0-1 Borussia Dortmund
3.19pmPierre-Emerick Aubameyang's header is the difference between the two sides as they head in at half time. Augsburg were unlucky not to equalise, creating two good chances shortly before the break.
3.21pmAugsburg have defended well to keep Robert Lewandowski quiet for much of the opening 45 minutes. However, Marco Reus will feel that he should have doubled the visitors' lead in the 41st minute, as he won the ball in space in the penalty area.
3.24pmMitchell Langerak has been impressive between the posts for Dortmund. After his teammates' strong start, he may have been expecting a quiet afternoon, but Augsburg tested the Aussie throughout. His hands will probably still be stinging from his save on the cusp of half time which kept out Raphael Holzhauser's long-range rocket.
3.27pmElsewhere in the Bundesliga, Leverkusen and Freiburg are level at 1-1, Hannover are leading Wolfsburg 1-0, Hertha Berlin have a 2-1 lead over Eintracht Freiburg and Hoffenheim are 1-0 up against Nuremberg.
3.31pmThe players are heading back out ready for the second half. Can Augsburg continue therr momentum from the end of the opening 45 minutes?
46 minAugsburg get the second half underway.
48 minAugsburg have started well, with Molders winning a free kick on the edge of the penalty area. Holzhauzer curled the ball in, but Reus was back to head the ball away from goal for Dortmund. Augsburg quickly win the ball back though, and are on the attack again.
49 minCHANCE! Molders loses the ball, allowing Dortmund to create their first chance of the opening half. Sahin breaks into the box, but scuffs his shot, giving Amsif a comfortable save.
51 minCHANCE! Aubameyang tries to add his second as he tries to slice the ball in from out wide, but Amsif make a brilliant save to deny to new signing. Hummels tries to head in from the following corner, but misses the target.
52 minBOOKING! Matthias Ostrzolek picks up the first yellow card of the game for a careless challenge on the goalscorer.
54 minAugsburg are focusing their attentions on getting the ball to Molders up front. The striker has looked sharp all game, but the Dortmund defenders are aware of his presence and marking him closely, limiting the hosts' chances to set up Molders.
56 minCHANCE! Baier tries a shot from around 25 yards out, but it takes a deflection on the way through and goes out for a corner. Augsburg initially clear the danger, but Reus looks to chip the ball back in. However, Klavan gets the ball away again.
58 minSUB! Jakub Blaszczykowski comes on for Ilkay Gundogan, who has been fairly quiet this afternoon.
60 minAltintop sends in a brilliant cross for Molders, but Subotic is on hand once again to ensure that the striker does not get a shot at the Dortmund goal. The Serbian has been superb at the back for Klopp's side this afternoon.
62 minCHANCE! Lewandowski looks to get himself involved, but he fouls Klavan, giving Augsburg a free kick around 30 yards out. Holzhauser delivers the ball right to Molders, but he mis-times his header, sending the ball just inches high of the crossbar.
63 minCHANCE! Reus immediately creates a chance for himself at the other end of the pitch, but his finish is hurried, and doesn't trouble Amsif.
65 minCHANCE! Schmelzer is brought down just outside the penalty area, giving Dortmund a free kick. Reus goes for goes from the set piece, forcing a stunning save from Amsif. Augsburg concede two corners as they try to clear the danger, but Amsif takes the ball at the third time of asking to halt the visitors' threat.
66 minGOAL! Augsburg 0-2 Borussia Dortmund (Aubameyang)
68 minReus quickly get the ball back in for Dortmund, and Aubameyang is waiting in the penalty area to smash the ball past Amsif, who had worked hard to keep the home side's deficit to just one goal.
71 minReus and Schmelzer work hard in midfield before picking out Lewandowski as they push for a third goal. The second has really lifted Dortmund, who are passing the ball around with more pace and confidence.
74 minAugsburg have let their heads drop since conceding the second goal. They're allowing Dortmund time and space on the ball. However, it looks like Weinzierl is getting ready to bring on some fresh legs.
76 minVerhaegh looks to take the ball into the box, but he is surrounded by Dortmund defenders, and they quickly take the ball away from the Augsburg captain. Reus leads the counter attack for Klopp's side, but it's cleared by Klavan.
78 minSUBS! It's a double change for Augsburg as Alintop makes way for Ronny Philp while Herzhauser goes off for Vlachodimos.
79 minGOAL! Augsburg 0-3 Borussia Dortmund (Aubameyang)
80 minAubameyang completed his hat-trick to complete a fantastic Bundesliga debut. Lewandowski picks out the Gabon international with a well-timed pass, allowing Aubameyang to round the keeper before tapping into an open goal.
81 minSUB! That's it from the hat-trick hero this aftenoon, as he makes way for Jonas Hofmann.
82 minCHANCE! Lewandowski also created a goal for himself moments after Aubameyang's third, but Amsif watched his effort all the way before comfortably stopping the ball.
83 minBOOKING! Moravek goes in the book for a clumsy challenge on Lewandowski.
84 minSUB! Andre Hahn, who has been superb in midfield for Augsburg, goes off for KEvin Vogt.
85 minPENALTY! Jan-Ingwer Callsen-Bracker brings down Lewandowski, who is lining up the spot kick.
85 minGOAL! Augsburg 0-4 Borussia Dortmund (Lewandowski)
87 minThe Polish forward finally gets his goal, from the spot and is immediately subbed off for Marcel Halstenberg
89 minDortmund aren't finished, despite their four-goal advantage. They're continuing to push forward against a tired Augsburg team.
90 minFULL TIME: Augsburg 0-4 Borussia Dortmund
4.21pmBorussia Dortmund comfortably win their opening game of the Bundesliga season thanks to a hat-trick from Aubameyang and a late penalty by Robert Lewandowski. The scoreline seems harsh on Augsburg, who kept themselves in the match for for best part of 70 minutes.
4.23pmAubameyang appears to have quickly settled into life in Germany, netting three times on his Bundesliga debut. Lewandowski was kept away from the goal for much of the game, but still managed to find the back of the net from the spot.
4.24pmWell that's all from the SGL Arena this afternoon, but stick around for reports from all of this afternoon's Bundesliga games. Thanks for joining me this afternoon, goodbye!