With the Spaniards 3-0 up from the first leg, Cristiano Ronaldo was left on the bench and after 17 minutes Dortmund’s Lukasz Piszczek handled to give the visitors a penalty. But Angel di Maria’s effort was saved at full stretch by Roman Weidenfeller.
Seven minutes later, that miss looked a lot bigger when Rues nipped in between Pepe and Real keeper Iker Casillas to slot into an empty goal.
And on 37 minutes, Robert Lewandowski’s curler was turned on to a post, only for Reus to smash home.
Henrikh Mkhitaryan had a chance to even the tie in the second half, but saw his shot hit a post from a tight angle.
The German side continued to throw everything at Madrid in the second half, hitting the woodwork and going close on a number of other occasions, but they could not find the third goal they needed as Carlo Ancelotti’s men held on for a 3-2 aggregate win.