Madrid entered the clash as the strong favourites to advance into the final four following a 3-0 victory when the pair met in the first leg at the Bernabeu last week.
Marco Reus scored twice in the first 45 minutes to take Dortmund to within one goal of the Spanish outfit in the tie.
However, it was not enough for the German outfit, who were eliminated 3-2 on aggregate.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
DORTMUND: Weidenfeller; Piszczek, Friedrich, Hummels, Durm; Kirch, Jojic; Mkhitaryan, Groskreutz, Reus; Lewandowski
MADRID: Casillas; Carvajal, Pepe, Ramos, Coentrao; Modric, Alonso, Illarra; Di Maria, Benzema, Bale
Borussia Dortmund vs. Real Madrid line-ups graphic. pic.twitter.com/JE8AhqoJEM— B/R Football (@br_football) April 8, 2014
Cristiano, vestido de calle, firma una camiseta a un seguidor del BVB pic.twitter.com/O4KGTlegwE— MARCA (@marca) April 8, 2014
50% - Robert Lewandowski has scored or assisted 20 of Dortmund's 40 goals in the #UCL since the start of last season. Essential.— OptaJose (@OptaJose) April 8, 2014