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Neuer then had to be quick off his line to foil a goal-bound Luis Suarez but was almost caught out by a cross-shot from Messi from the right which drifted through the area and struck the post.
But just as Barca seemed to have established themselves, the Germans regained their lead in the 21st minute — Serge Gnabry fed Perisic on the left and the Croatian glanced up to see his options before drilling past Marc-Andre ter Stegen.
Bayern then added the third as Barca’s defense was opened up again with ease. Thiago Alcantara was given plenty of space in midfield to find Leon Goretzka whose superb ball picked out Gnabry, who had got behind Lenglet and then made no mistake with the finish.
Flick’s side were running riot and it got worse for Barca when a low cross from Joshua Kimmich was turned in at the near post by Mueller — another goal of ruthless simplicity making it 4-1 at the break.
The Spaniards desperately needed to find a way to shift the momentum after the break and Suarez, one of the few Barca players to emerge with any credit from the encounter, provided a route back into the game with a fine strike, in the 57th minute.
Jordi Alba found Suarez on the edge of the box and the Uruguayan jinked passed Jerome Boateng before blasting home.
But Bayern were in no mood to turn down the heat and six minutes later they restored their three goal advantage thanks to some outstanding work from their Canadian teenager Alphonso Davies.