The recently-crowned German champions were full value for their comprehensive success with Thomas Muller scoring twice and Mario Gomez and Arjen Robben both on target against a disjointed Barca, for whom Lionel Messi was anonymous on his return from a hamstring injury.
Barcelona may have dominated possession, as they do so often, but their brittle defence was ruthlessly exposed by the rampant hosts while their much-vaunted attack was rendered impotent with Manuel Neuer barely having a save to make throughout the contest.
Robben came close to breaking the deadlock in only the second minute when a neat exchange of passes with Javi Martinez saw the former Chelsea man bring a diving save from Victor Valdes.
Bayern's appeals for a penalty in the 15th minute were turned away by referee Viktor Kassai as Philipp Lahm's long-range effort struck Gerard Pique on the arm as he turned away inside the box.
The home side took the lead with 25 minutes gone when Robben's cross from the right was headed back across the goal by the excellent Dante, with Muller arriving at pace to head down and beyond Valdes.
Bayern appealed for a penalty once again in the 33rd minute when Franck Ribery's corner was met by Dante's head before striking the arm of Alexis Sanchez as he challenged the defender, but Kassai and his assistants were again unmoved.
Jupp Heynckes' men doubled their advantage early in the second period when Robben's corner left Valdes in no-man's land, with Muller heading the ball back across for Gomez to complete a simple finish, although with a hint of offside.
Robben and Ribery threatened to increase their lead before a brief spell of Barcelona pressure, but again Neuer was never truly tested, aside from one relatively routine stop from Sanchez, with his defence standing firm against the probing of the visitors.
The Dutchman made it 3-0 in the 73rd minute, but there was a huge amount of controversy over his strike as Muller's blatant body-check on Jordi Alba, under the nose of the additional official on the goalline, allowed his team-mate the space and time to fire beyond the exposed Valdes.
Barcelona's miserable evening was summed up when defender Marc Bartra made a complete hash of his shot when he was found in acres of space behind the home defence from Xavi's clever free-kick.
And the rout was completed eight minutes from time as Bastian Schweinsteiger, Ribery and David Alaba combined down the left before the latter's dangerous low cross was turned home by a gleeful Muller.
After the match, goalscorer Robben refused to accept that Bayern Munich are on course for the final despite their crushing victory over Barcelona.
He told Sky Sports: "That is the strength of this team, we will keep focusing, there is always the next game. Let's stay concentrated, not talk too much and just play our football."
And Barcelona assistant manager Jordi Roura insisted they will not give up on their European dreams despite the humiliating defeat.
He said: "We have to compete in the second leg and try to win. We will give it our all. We lacked the freshness to compete with them which is something we have to look at."