Thomas Partey's own goal gave Leverkusen a first-half lead, though, before Kevin Volland's strike secured a first win in a Champions League group game for Peter Bosz at the 10th time of asking.
Alvaro Morata got a late consolation after Nadiem Amiri had been sent off.
Atleti have struggled in attack in recent weeks and offered little threat to Lukas Hradecky's goal in the first half, with centre-back Felipe coming close to an own goal when he flicked a corner onto the crossbar.
Just four minutes later, Atleti failed to clear their lines after Jan Oblak punched a corner off the line, with Thomas completely miscuing his defensive header to send the ball into his own net.
4 - Only 1 of @bayer04fussball's last 5 Champions League goals was scored by a Leverkusen player (Karim Bellarabi vs Atletico Madrid in 2016-17), the other 4 were all own goals. Support. #B04Atleti pic.twitter.com/UHVx3aTF7B— OptaFranz (@OptaFranz) November 6, 2019
It was the fourth Champions League goal for Leverkusen to be scored by an opposition player out of the last five, but there was little by way of mere fortune about their second, Volland controlling Karim Bellarabi's cross before rifling a low shot past Oblak.
Morata turned the ball in from Vitolo's cross only to be correctly ruled offside, as Atleti's late pressure could not prevent their 11-game unbeaten run in all competitions from coming to an end.
The match ended in tempestuous fashion, with four players booked after a melee in the Atleti penalty area and Amiri shown a straight red card for a poor challenge on Santiago Arias.
Morata pulled a goal back in additional time, gathering Thomas' throughball and finishing emphatically past Hradecky, who then stuck out a leg to deny the striker an equaliser with almost the last kick of the game.
What does it mean? Leverkusen still alive as Atletico are made to wait
Atletico would have joined Juventus in the next round with a win here, but the defeat means they are only four points above Lokomotiv and Leverkusen.
While progress to the last 16 is still very much in their own hands, another loss in Turin on matchday five will make for an anxious final game at home to Lokomotiv on December 11.
Hradecky holds firm
Atleti only really began to threaten at 2-0 down, but Hradecky made seven important saves to preserve their lead, including a vital stop in practically the final second.
Pouting Thomas sums up listless Atleti
Thomas got his header spectacularly wrong, giving Leverkusen the edge, and he seemed still to be dwelling on his error when he made little effort to close down the space on the Atleti left in the build-up to Volland's goal. He did get a late assist, at least.
Key Opta facts
- Atletico Madrid have lost five of their last six Champions League away games against opponents from Germany (W1), conceding six goals and scoring just once.
- Alvaro Morata has scored in five consecutive games in all competitions (five goals) for the first time in his club career.
- Thomas Partey is the fourth Atleti player to score an own goal in the Champions League, and the first since Stefan Savic against Chelsea in December 2017.
- Diego Simeone's side conceded 15 shots against Bayer Leverkusen, their most in a game this season in all competitions.
- Diego Costa had nine touches against Leverkusen, none in the opposite box. That is his worst tally in a Champions League game for Atletico since the 2014 final against Real Madrid, when he played just six minutes.