The Spanish giants controlled proceedings as they sought revenge for last season's semi-final loss to the Germans which appears, at this stage, to be successful.
The lead was doubled when Xabi Alonso won possession on the edge of the area with the ball falling for Isco who took a couple of touches before passing a side-footed effort past Weidenfeller and into the back of the net.
Just before the hour-mark, Cristiano Ronaldo made history when he equalled Lionel Messi's record of 14 goals in a Champions League campaign when he got on the end of a Luka Modric through ball before dazzling with quick feet and finishing with customary ease from close range.
The three-goal victory was well-deserved by Carlo Ancelotti's Blancos while Juergen Klopp's BVB will more than likely find the deficit hard to overcome when the two sides reconvene at Signal Iduna Park next week.
It keeps alive Real's pursuit of a 10th European title which they have waited more than a decade to achieve following their 2001/02 triumph over Bayer Leverkusen in Glasgow.
2013/14 UEFA Champions League - quarter-final first leg
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