Bayern were undone by an attacking tidal wave soon after, with Daniel Van Buyten scoring at the wrong end then Ilkay Gundogan made it 3-1 seconds later.
Robben reduced the deficit but substitute Pierre-Emerick Aubameyang teed up Reus for a fourth as Dortmund rallied to victory.
And it was the energetic playmaker who gave Dortmund the lead following an edgy opening to the match at Signal Iduna Park six minutes in.
Robert Lewandowski, the subject of fierce interest from Bayern over the summer, saw his cross helped on by Sven Bender, whose seemingly tame header was flapped at by Tom Starke, allowing Reus to head into the net.
Bayern, already behind failed to recover from that initial setback, and were lucky not to have gone 2-0 down as Lewandowski raced through past David Alaba, to slot home under Starke, before being pulled back for a debatable offside call.
Nevertheless, the European champions began to settle into their rhythm and posed Dortmund a few problems.
Shaqiri fired a low shot towards Weidenfeller, who was forced into a fantastic double save seconds later as the Swiss international was thwarted along with Thomas Muller with the unsuccessful follow-up.
Jurgen Klopp's side continued to search for their second and were again denied by Starke. Gundogan fed through Reus on the edge of the area, squaring into the middle for Lewandowski who was beaten by the sprawling legs of the goalkeeper.
For all of their perseverance, Bayern equalised early into the second half after a dazzling spell. Philipp Lahm's superb cross was met by the head of Robben, who after scoring the winning goal of the Champions League final, punished Dortmund here again with the leveller.
But Dortmund were unperturbed, and swiftly regained the lead after a superb counter-attack which resulted in Daniel Van Buyten deflecting the ball into his own net. Seconds later, it was 3-1 after Gundogan's curling effort beat the defence and Starke, allowing for a third goal scored in little over a minute and a half of frenzied action.
Bayern, though, continued to go for the jugular after yet another setback and were back in sight after another bit of fine work by Lahm on the wing. The Germany captain's teasing low ball picked up Robben, who deftly beat those around him and Weidenfeller to reduce the deficit.
At the other end, die Roten were also profligate in front of goal, as another golden chance went begging. Shaqiri this time with a fine pass into the path of Alaba, whose teasing low ball evaded Mandzukic by inches before Thomas Muller was undone by the crossbar in a brilliant conclusion to the game.
However, Dortmund - who squandered countless chances late on, finally saw themselves over the line with a blistering counter-attack. Lewandowski set off Aubameyang, who teed up Reus for a superb fourth to seal the first trophy of the German football season.