The runaway Bundesliga leaders have been flattening everything in their path for most of this season while Arsenal have struggled to keep pace with the Premier League's big guns while suffering some humiliating domestic cup defeats.
The gulf in confidence and class was obvious as goals by Toni Kroos, Thomas Muller and Mario Mandzukic earned Bayern their first ever win in London to make them overwhelming favourites to reach the last eight.
On this form, it will take a good side to stop four-times European champions Bayern returning to North London in May at Wembley to contest a third Champions League final in four seasons.
"Here in England it has been hard for Bayern in the past," coach Jupp Heynckes, who will make way for Pep Guardiola at the end of the season, told reporters.
"We've scored three goals in an away game, that's quite good. I think Arsenal allowed us quite a few things in their defence but we are in astonishing form at the moment and we can punish the smallest mistakes of opponents."
Oozing confidence after an 18-match unbeaten sequence which sees them 15 points clear at the top of the Bundesliga, Bayern had seized control of the match before the midway point of the first half with Kroos and Muller both on target.
VERY DIFFICULT
Arsenal did rally after the break with Lukas Podolski cashing in on a rare piece of generosity from the visitors but just when Arsene Wenger's side looked as though they might restore parity, Mandzukic put Bayern out of reach again.
"Let's not hide from the fact that it will be very difficult [to win the tie]," Wenger, who is under increasing pressure from fans and in the media, told reporters. "They haven't played in two finals in three years for no reason.
"We played against a side with no doubts, with everything positive, and that's not the case with us at the moment."
"We put in a good battle in the second half and looked like we could get it back to 2-2 but to go 3-1 was a big blow for the team and we could have conceded more."
Determined to make amends for a 1-0 defeat by second tier Blackburn Rovers in the FA Cup Fifth Round on Saturday, Wenger's side began positively with Santi Cazorla and Theo Walcott advancing deep into Bayern territory.
Their apparent confidence proved to be an illusion, however, once Bayern struck after seven minutes.
Muller, a constant menace down the right flank, was allowed time to cross and his scuffed delivery wrong-footed Arsenal's defence and fell perfectly for Kroos to swivel and thump a first-time shot into the turf and past keeper Wojciech Szczesny.
Sensing Arsenal's unease, Bayern doubled their advantage after 21 minutes when Daniel Van Buyten's glancing header from a corner was blocked on the line by Szczesny but the ball popped up for Muller to flick it into the unguarded net.
ARSENAL FRUSTRATION
Bayern looked capable of putting the tie to bed before half-time and almost did so moments before the break
