The German champions plundered four goals in each half to reach the semi-finals in sensational fashion.
Hans-Dieter Flick's irresistible side became the first ever to score eight in a UEFA Champions League knockout match as they blew away the five-time winners in Lisbon.
Match in brief
Thomas Müller gave Bayern the lead after beautifully exchanging passes with Robert Lewandowski but that was quickly cancelled out when David Alaba sliced Jordi Alba's cross into his own net. Lionel Messi hit a post but Barcelona then wilted under a ten-minute onslaught.
Serge Gnabry robbed Sergi Roberto and teed up Ivan Perišić for Bayern's second and the floodgates opened. Gnabry himself added the third and Müller turned in Joshua Kimmich's cross to make it four in the 31st minute.
Luis Suárez reduced arrears but that only disturbed the hornets' nest again, Kimmich making it 5-2 following a dazzling run by Alphonso Davies. Lewandowski's 14th goal of their European campaign and a late Philippe Coutinho double against his parent club sealed a landmark victory.
Man of the match: Thomas Müller (Bayern)
Cosmin Contra, UEFA technical observer: "Müller takes the award because he scored two goals, found space between the lines, worked hard defensively. Good attitude. A leader out on the pitch."
Graham Hunter, Barcelona reporter
How often have Barcelona been THAT glad to hear a final whistle? Even hanging on for a vital win it's rare to see them need the referee to end a contest like they needed that finish to proceedings there. This is a genuinely epoch-making defeat, a margin which will embarrass Barcelona hugely and begin a cathartic process of change and re-evaluation. It must. Kudos to Bayern, they've beaten a side full of winners and champions by a huge margin.
Jordan Maciel, Bayern reporter
We've never seen anything like this before, we'll likely never see anything like it again. A scoreline that reads like a comfortable two-legged tie, against one of the giants of European football. If you weren't backing Bayern before, you certainly will now. Breathtaking from La Bestia Negra.
Thomas Müller, Bayern forward: "We worked so hard, with such intensity, it's tough for anyone to beat us. We had so much fun out there today. Barcelona have special players and we had to be even more aggressive, come back again and again. It's a big statement but the semi-final starts at 0-0."
Leon Goretzka, Bayern midfielder: "It's difficult to put this into words so soon after the game. I think it will take a couple of days to process this result. We have so much confidence, but as we just said in the changing room we've taken the first of three steps."
Gerard Piqué, Barcelona defender: "I'm in pain. We all are. We can't compete like that. It's very, very tough to take. We must change the dynamic we are on. Is it an end of an era? I'm not sure but I know that we must accept that we have hit the bottom."
- Bayern score eight in a UEFA Champions League match for the first time.
- This is the first time Barcelona have conceded six goals or more in a European game, and the first time they have shipped four goals in the first half of a UEFA Champions League match.
- This is the fastest a team has ever scored four goals in a UEFA Champions League knockout match – Bayern beating their own record of 36 minutes, set against Porto in the 2014/15 quarter-final second leg.
- Bayern have won 27 and drawn one of their last 28 competitive matches.
- Thomas Müller has scored six goals, in five appearances, against Barcelona in the UEFA Champions League – more than any other player.
Barcelona: Ter Stegen; Semedo, Piqué, Lenglet, Alba; De Jong, Busquets (Fati 70), Roberto (Griezmann 46); Vidal; Messi, Suárez
Bayern: Neuer; Kimmich, Boateng (Süle 76), Alaba, Davies (Hernández 84); Thiago, Goretzka (Tolisso 84); Gnabry (Coutinho 75), Müller, Perišić (Coman 67); Lewandowski
Bayern will take on Lyon in the last four. Their single-leg semi-final will kick off at 21:00 CET on Wednesday 19 August and be held at the Estádio José Alvalade in Lisbon.