The Spanish giants were chasing what would be a record third straight triumph in Europe's elite club competition.
The decisive clash here on Tuesday in front of 80,000-plus at the Santiago Bernabeu between the two giants of European football delivered plenty in the way of excitement, Efe news reported.
Leading 2-1 after the first leg in Munich, the hosts conceded in the third minute, when a poor clearance by Sergio Ramos led to Joshua Kimmich's second goal of the tie.
Seven minutes later, it was the turn of Bayern defender David Alaba to err at his team's expense.
The Austrian left Benzema free to redirect Marcelo's cross to make it 1-1 on the night and 3-2 overall in Real Madrid's favour.
Suddenly looking less dangerous, the visitors concentrated on defending and forced the Blancos to rely on long balls to get deep and chances were scarce for both sides.
With Cristiano Ronaldo unmarked, Marcelo instead passed to Toni Kroos, while both Thomas Maller and James Rodriguez wasted opportunities for Bayern.
The closing seconds of the first half saw the referee decline to award a penalty for a clear hand ball by Marcelo on an effort by Kimmich.
Benzema struck again for Real Madrid in the first minute of the second half, taking advantage of a colossal blunder by Bayern keeper Sven Ulreich to send the ball rolling into the empty net to consolidate the advantage for the hosts.
But anyone who expected Bayern to roll over and die was quickly disillusioned as the German side laid siege to Blancos' goal.
Real Madrid keeper Keylor Navas delayed the inevitable as long as he could, making a fine stop against Alaba and diving to thwart Mats Hummels before finally giving up a goal to former Blanco James, who scored in the 62nd minute.
The final 28 minutes were torment for the Blancos and their fans as Bayern flew forward to get the equalizer, but the home side survived the onslaught and were headed to Kiev with thoughts of making history yet again.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
