Ilkay Gundogan then followed that up with another goal just a minute later, finishing off a spell of three goals in as many minutes.
Robben pulled a goal back for his side just after the hour mark, but Dortmund put the game to bed through Reus's second of the evening five minutes from time.
Here, Sports Mole takes an in-depth look at 90 minutes of highly-entertaining football.
On target 7
On target 8
Was the result fair?
On the overall balance of play, probably not. It was an even match for most of it, but Dortmund were caught out less in defence. Bayern looked vulnerable to counter-attacks and that is where Dortmund excelled. In terms of clear chances, Dortmund definitely deserved to win, but Bayern will feel slightly hard done by after this result.
Brilliant. They have established themselves as one of the most exciting teams in Europe over the past few seasons and continued that this evening. Their counters were lightning quick and they always broke in numbers, which caught Bayern out on more than one occasion. Their defence stayed firm for the vast majority of the match, limiting Bayern to very few clear chances. If they continue like that this season, they will be serious challengers to regain the Bundesliga title.
Bayern Munich's performance
Munich also put in a very good performance, but they were unable to break down the Dortmund defence on as many occasions. Their defence looked a little shaky at times, particularly Starke in goal, but on the whole it was another impressive performance. If anyone edged overall play throughout the match, it was Bayern; they managed to have the lion's share of possession despite Dortmund's heavy pressure and tireless work rate.
Sports Mole's man of the match
Marco Reus: With Mario Gotze leaving Dortmund to join Munich, even more pressure falls onto the shoulders of Reus, and he showed today that he can deal with it. He was involved in everything good Dortmund did in an attacking sense and was one of the main counter-attacking threats that plagued Pep Guardiola's side. His first goal was a gift but he showed good determination to not give up on it when everyone else had, while he was still racing forward to support the front men for his second goal in the 86th minute.
There is only one winner here: Tom Starke. The reserve keeper got off to the worst possible start when he somehow spilled the easiest of catches straight into the path of Reus, who took full advantage to give Dortmund the lead after just six minutes. It was a terrible piece of goalkeeping.
Jochen Drees was in the relatively privileged position of not having to take his decisions too seriously as this match still counts as a pre-season, but he did not shy away from making decisions either. His one and only yellow card came in the 91st minute and he tried his best to allow a fast-tempo match to flow freely.
Dortmund: Next up for Dortmund is the German Cup first round where they will face Wilhelmshaven.
Bayern Munich: Bayern, meanwhile, have a pre-season friendly against Sao Paulo on Wednesday before their first round match against Schwarz-Weiss Rehden in the German Cup.