Dortmund had gone in ahead at the break thanks to a Marco Reus volley and Alvaro Arbeloa own goal but were bombarded in the second half and eventually had their hearts broken by Ozil's free kick, which Roman Weidenfeller could have dealt with much better.
Here, Sports Mole casts it eye over an enthralling 90 minutes in the Spanish capital.
On target 11
On target 5
Was the result fair?
Over the whole game, yes. Dortmund's swift counter-attacking and some lax Madrid defending made the German champions look the home side in the opening half but they inevitably sat back and invited pressure in the second.
Not great. Jose Mourinho didn't show any emotion when Ozil found the net late on and that is surely down to the poor showing his men put in. Cristiano Ronaldo had a real off day while at the back some of the Madrid defending was simply amateur. Staying goalside of your man is a basic football principle and it was ignored for both the Dortmund goals.
Very impressive in a daunting colosseum like the Bernabeu. Jurgen Klopp's side were scintillating going forward in the first 45, with Robert Lewandowski winning headers and Marco Reus and Mario Gotze offering plenty of support. Their attack lost its legs in the second period and they will be crushed to concede from a set piece in the dying moments.
Sports Mole's man of the match
Ilkay Gundogan: The Borussia defensive midfielder may have come off with 10 minutes to play but he was instrumental in Dortmund's resolution in the 80 minutes he was on the pitch. The German also supported the front three when he could, especially in the opening period. A real box-to-box display from the 22-year-old.
Has to go to Weidenfeller. With just a minute of normal time remaining, the goalkeeper moved sluggishly towards his left-hand post and then seemingly thought Ozil's free kick was going wide only to see it clip the foot of the post and creep in.
Cuneyt Cakir was superbly consistent. On many occasions the likes of Angel di Maria went down far too easily but Cakir was unmoved, waving away the appeals of the dumbfounded superstars. There were a couple of possible penalty appeals from both sides but the Turkish official stuck to his tough guns.
Real: Madrid travel to Levante in the league on Sunday looking to keep up the pressure on Barcelona at La Liga's summit.
Dortmund: BVB, meanwhile, go to the Bundesliga's bottom side Augsburg on Saturday.