The visitors were sent on their way by two goals in the space of four minutes from Sergio Ramos in the first half as Bayern struggled to deal with Real's set pieces.
Cristiano Ronaldo added a third for Madrid 10 minutes before the break as he finished off a slick counter-attack, while he grabbed his record 16th Champions League goal of the season in the 90th minute to seal a 5-0 aggregate win.
Here, Sports Mole takes an in-depth look at a remarkable night at the Allianz Arena.
On target: 4
On target: 5
Was the result fair?
Absolutely. Bayern may have dominated the possession, as they usually do, but just like in the first leg they lacked penetration and Madrid dealt with their pressure fairly comfortably throughout. The majority of Bayern's possession came in the second half too, when the visitors had taken their foot off the pedal.
It was another tactical victory for Carlo Ancelotti over Pep Guardiola as the Madrid boss carved Munich apart on the counter-attack. He was helped in that regard by the two goals that came unexpectedly from set pieces, leaving Bayern with little option but to go all-out attack.
In truth, it could have been more than four for Real tonight. They missed a couple of other good chances throughout the match, while Bayern's clear openings were very limited despite their relatively high shot count.
It should not be forgotten that some were hailing this Bayern Munich side as one of the greatest teams of all time a little over a month ago, but since clinching the Bundesliga title there is no doubt that they have gone off the boil. They seemed short of ideas at times tonight and the lack of a 'Plan B' was all too evident as Madrid looked like they could defend against the passing movement all night, with Bayern struggling to move up a gear.
They actually started the match fairly well, injecting the sort of pace and urgency into their attacks that was lacking in the first leg. However, defensively they were a shambles and, with players like Gareth Bale and Cristiano Ronaldo in the opposition team, that is always going to be a recipe for disaster.
The introduction of Javi Martinez at half time did improve things for the hosts, who had been picked apart at will in the first half, but all four of Madrid's goals could have been defended better. It was earmarked as a weakness going into the game, and Madrid exploited it fully.
Real Madrid's performance
Real Madrid have had countless great nights in their illustrious history, but this will be right up there with the best. To systematically take apart a team like Bayern Munich and to deserve such an emphatic victory away from home against the defending champions is a remarkable feat and one that they will justifiably be proud of.
Defensively they were solid again as Bayern struggled to play through the back four. Ramos and Pepe resisted everything that was thrown at them, while Fabio Coentrao and Daniel Carvajal also dealt with the significant threat of Franck Ribery and Arjen Robben. At the other end, they were irresistible at times as they cut through the Bayern defence with swift and slick counter-attacks.
Such a performance will certainly make them favourites to beat either Chelsea or Atletico Madrid in the final on May 24, while it should also give them the confidence to catch Atletico in La Liga - although that one is out of their own hands. 'La Decima' is now within their sights, and a similar performance to tonight's in Lisbon will surely see them clinch that 10th title.
Sports Mole's man of the match
Sergio Ramos: A number of Real Madrid players could make a valid claim to this title tonight, but Ramos gets the nod for the work he did at either end of the pitch. Alongside Pepe, he was instrumental in dealing with anything Bayern came up with, making numerous important challenges and clearances.
Then, of course, he scored the opening two goals, which put the tie completely in Madrid's control. While a third was perhaps needed to kill Bayern off, Ramos's quickfire double took the fight out of the hosts and sent his side on their way to a remarkable result.
Bayern's defending for each goal was suspect, but the gaffe of the game goes to Xabi Alonso for an action that he will still be kicking himself over. With his side 3-0 up and cruising, he slid into a needless challenge on Bastian Schweinsteiger, who was not in a particularly threatening position.
The referee had little option but to show the Spaniard a yellow card, which rules him out of the final next month. Alonso knew the significance of the card, and the disappointment on his face was clear to see, but it was a moment of madness from the 2005 Champions League winner so he only has himself to blame.
All of the focus tonight was on the football, which is how it should be on such occasions. Pedro Proenca did not have many big decisions to make, and in general he controlled the game well at times when it threatened to bubble over.
One incident the officials did miss, however, was a Ribery slap on Carvajal inside the area that would have been a certain red card for the French winger had he been caught.
Bayern Munich: Next up for Bayern is a trip to face Hamburg in the Bundesliga on Saturday afternoon.
Real Madrid: Madrid, meanwhile, resume their title challenge against Valencia at the Bernabeu on Sunday evening.