The result has left Atletico in third spot in Group B on five points, four points behind second-placed Porto, while Leverkusen are fourth, one point behind their opponents in Spain.
As a result, the two teams will battle for the Europa League spot in the section, with Club Brugge and Porto both advancing to the round of 16 from the section.
Atletico had a golden chance to win it late on from the penalty spot following a VAR check, but Yannick Carrasco's effort was saved by Lukas Hradecky before Saul Niguez struck the crossbar and the ball was then cleared off the line in incredible scenes.
Leverkusen made the breakthrough in the ninth minute of the contest, with Moussa Diaby collecting a pass from Adam Hlozek before finding the back of the net past Jan Oblak.
Atletico could have levelled in the 12th minute when Angel Correa worked his way into the away side's penalty area, but the attacker's effort was well saved by Hradecky.
Diego Simeone's team did manage to equalise in the 22nd minute, though, when Carrasco picked out the bottom corner with a brilliant strike from the edge of the box.
Leverkusen answered straight back, with the Bundesliga outfit regaining the lead in the 29th minute courtesy of a goal from Callum Hudson-Odoi, who finished past Oblak after collecting a pass from Nadiem Amiri.
Alvaro Morata had an opportunity to make it 2-2 in the 34th minute when he met a cross from Antoine Griezmann, but the Spain international's effort was wide of the post.
Leverkusen had the final chance of the first half when the ball fell kindly for Diaby at the edge of the box, but the Frenchman's effort was just too high, with Atletico looking shaky at the back.
Atletico levelled the scores in the 50th minute through Rodrigo De Paul, with the half-time substitute finding the back of the net after smart work from Carrasco.
Simeone's side twice came close to a third through Griezmann before the hour, and the La Liga side were dominating the contest approaching the final 20 minutes of action.
Leverkusen were always dangerous on the break, though, and Oblak had to make a smart save to keep out an effort from Diaby in the 75th minute of the contest.
Hradecky then had to keep out a volley from Griezmann down the other end to prevent Leverkusen from conceding a third at Wanda Metropolitano.
Atletico had a brilliant chance to keep their last-16 hopes alive late on, but Carrasco missed his penalty following a handball before Leverkusen survived two dangerous moments in the same incident, with the two teams now left to battle for third spot in the group.