Lennart Karl was among the standout performers, recovering from a frustrating opening period to put the visitors ahead nine minutes after half-time.
The 18-year-old took advantage of Robin le Normand losing possession, darting beyond the Atletico defender before delicately lifting the ball over Jan Oblak to break the deadlock.
Konrad Laimer subsequently extended Bayern's advantage with an emphatic finish. Harry Kane supplied the assist, picking out the midfielder in space before Laimer unleashed a ferocious strike that flew beyond Oblak and nestled in the roof of the net.
Kane, meanwhile, endured an uncharacteristically quiet evening in his first European outing since receiving the Ballon d'Or. The England international had found the net in each of his previous 10 Champions League appearances but missed the opportunity to match Cristiano Ronaldo's competition record. He failed to register a shot on target, sending an acrobatic attempt wide before also dragging another effort off target.
Oblak prevented the scoreline from becoming more damaging with an impressive intervention to turn Dayot Upamecano's deflected strike onto the crossbar. At the opposite end, Manuel Neuer had little to do, facing just one effort on target throughout the contest.
Die Roten boss Vincent Kompany is still recovering from illness. Assistant coach Aaron Danks took charge for the game.
"I'm very pleased with the team's performance," said Danks.
"The way we kept a clean sheet and created chances in attack was impressive. It's difficult to pick out individual players; it was just a superb team performance."
He added: “There was a lot of noise around us, but the team showed incredible focus and character to deliver a top-level performance at a venue as difficult as this.”