Seeking a reaction after Saturday's shock FA Cup exit at the hands of second-tier Blackburn Rovers, Arsenal were instead soundly beaten by a Bayern side desperate to atone for last season's Champions League final heartache.
Bayern, runaway leaders in the Bundesliga, bossed the first half of the last 16 first leg, and went in 2-0 up at half-time through goals from Toni Kroos and Thomas Mueller.
Lukas Podolski replied early in the second half, breaching his former club's defence for the first time in 2013, but Mario Mandzukic struck late on to put Bayern firmly in control ahead of the second leg on March 13.
"We put in an outstanding performance over a long period of time against one of the top teams in Europe," Kroos told German television channel Sky.
"We really dominated, and I didn't see any big chances from Arsenal, but it was annoying to concede the goal."
With defeat, Arsenal's hopes of ending an eight-year trophy drought recede still further, and although Bayern will be without the suspended Bastian Schweinsteiger in the second leg, with three away goals, they may not miss him.
"In the second half, we stepped it up and it's unfortunate we didn't do that in the first half," Arsenal midfielder Jack Wilshere told British television channel ITV.
"I'm not sure why. Maybe it's a bit of nerves or anxiety, because we show what we can do when we play. We will look at it and try to put it right."
Greeted by roars from the home fans as they left the tunnel, Arsenal began with intent, and saw first Santi Cazorla and then Theo Walcott thread inviting crosses into the Bayern box from the right.
However, the wind was sucked from their sails in only the seventh minute as Bayern took the lead from their first attack.
Mueller's cross from the right eluded the stretching Mikel Arteta and Kroos beat Per Mertesacker to the bouncing ball to hit a crisp half-volley that skipped off the turf and flashed past the flailing Wojciech Szczesny.
It was a cruel blow for Arsenal and things got even worse in the 21st minute, with Mueller volleying into the roof of the net from close range after Szczesny parried Daniel Van Buyten's header from a right-wing corner.
Bacary Sagna and Arteta found their way into the referee's book as the hosts' frustrations threatened to get the better of them, while Bayern's fans launched a gleeful chorus of the English terrace chant, 'Football's coming home!'
Mandzukic almost put Bayern out of sight when he directed a header inches wide of Szczesny's right-hand post shortly before half-time.
Bayern retreated in the second half, content to look for opportunities on the break, but it backfired in the 55th minute as Arsenal pulled themselves back into the match.
Wilshere's looping corner from the Arsenal right was somehow allowed to bounce in the heart of a crowded area and Podolski exploited hesitancy in the visiting ranks to nod a header past flat-footed Germany team-mate Manuel Neuer.
Szczesny had to tip a rising drive from Kroos over the bar as Bayern resumed their assault on the home goal, with Javi Martinez heading over from the ensuing corner.
Arsenal manager Arsene Wenger introduced Tomas Rosicky and Olivier Giroud in the 72nd minute and the pair almost made an immediate impact.
Rosicky found Walcott wide on the right with a strafing pass and Giroud met the Englishman's subsequent cross with a first-time shot that Neuer scrambled away.
It proved an illusory glimpse of hope. Five minutes later, substitute Arjen Robben released Philipp Lahm on the overlap and the Bayern captain's low cross was bundled in by Mandzukic.