Thomas Muller headed the recently-crowned Bundesliga champions ahead in the 25th minute and Mario Gomez turned in the second goal amid suspicions of offside early in the second half.
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Arjen Robben added a third in the 73rd minute and Muller then grabbed his second of the night as Barca collapsed dramatically in a game where Lionel Messi, returning from a hamstring injury, made little impact.
In doing so, Bayern avenged their defeat by the same score in the quarter-finals four years ago.
Robben nearly put Bayern ahead in the third minute after a clever backheel by Javi Martinez gave him a clear scoring chance but he shot straight at keeper Victor Valdes.
Barca then put together some intricate passing moves although they rarely threatened to score and Bayern had the next chance when a goalbound Philipp Lahm shot was blocked by defender Gerard Pique.
Pique also appeared to handle when he cleared the resulting corner but the referee was not interested.
It was not long before Bayern, who won the Bundesliga with six games to spare, went ahead with the help of an overhit corner by Franck Ribery.
His effort found Robben on the other side of the penalty area and a rare right-footed cross from the Dutchman found Dante whose header fell for Mueller to stoop and score.
Barca's most dangerous first-half effort was a low Pedro cross which Dante was lucky not to turn into his own net.
Bayern extended their lead from another corner as Mueller at the back post headed back into the middle for Gomez to turn the ball in at close range after 49 minutes although he may have been fractionally offside.
The Germans threatened another as shots from Mueller and Ribery flashed wide and then Robben headed wide from a free kick.
Barca, often reduced to long balls forward, managed to impose some of their possession football but were vulnerable on the break.
Robben exploited the gaps when he burst down the right for the third and, with Barca still reeling, Mueller blasted a David Alaba pass into the net for the fourth goal.
The rout equalled Barca's worst ever defeat in European competition.
