The Bhoys beat Anderlecht by the same scoreline in their last Group B outing, but, as they did with Paris Saint-Germain, found the German champions to be a bridge too far.
Bayern should have further punished Celtic as Craig Gordon pulled off a series of second-half saves, but the visitors were unlucky not to score themselves when Scott Sinclair saw an 88th-minute goal disallowed.
Relive how the action unfolded with Sports Mole's minute-by-minute commentary.
Subs: Starke, Sule, Friedl, Rafinha, Tolisso, Vidal, James
Subs: De Vries, Bitton, Dembele, Rogic, McGregor, Forrest, Ajer
The way that Manchester City are playing, it would be brilliant to see Guardiola return to Munich later in this year's competition.
He told reporters: "You see the transfer window and how crazy it has become...clubs like Celtic and others like Anderlecht can't keep up. But I would never make the mistake of under-estimating Celtic.
"Celtic are a physical, aggressive team. They have a lot of experience and they have won the Scottish Premiership six times in a row. They also have a great coach in Brendan Rodgers and have a great history in Europe but we want to qualify for the next round."
"We have a duty to play our game," Rodgers told The Guardian. "That is what we have already spoken of. Our disappointment against Barcelona and PSG was that we didn't quite impose our way of working. So our message is we have a duty to play how we play and that is to attack and be aggressive."