Atletico entered the match holding a 4-2 lead from the first leg in Germany last month, and that score still stood at the end of the reverse match as Diego Simeone led his side into the last eight of the competition once again.
Gabi and Filipe Luis both missed out for Atletico through suspension, which opened spots in the team for Lucas Hernandez and Thomas Partey. Angel Correa was also handed a start, while Fernando Torres was back on the bench for the hosts, two weeks after being discharged from hospital with a head injury.
As for Leverkusen, Jonathan Tah, Lars Bender, Omer Toprak and Stefan Kiessling remained on the treatment table, Benjamin Henrichs was suspended, while Kai Havertz missed out due to "important exams at school". Tin Jedvaj was fit after missing the first leg, however, while Julian Baumgartlinger and Kevin Volland were both handed spots in the XI.
It was the visitors that came closest to making the breakthrough in the early stages, but Volland, who had been found by a pass from Kevin Kampl inside the Atletico box, could only fire wide of the post after turning away from Jose Gimenez with a fine piece of skill.
Atletico's first chance of the night arrived in the 15th minute when Correa found some space inside the Leverkusen box before attempting to pick out the bottom corner, but Jedvaj's block stopped the ball from finding the back of the net.
Hernandez was next to come close for Leverkusen in the 22nd minute after a smart cross from Julian Brandt, but the Mexican's effort flew over Jan Oblak's goal as the score remained goalless on the night approaching the mid-point of the first period.
Baumgartlinger, who took it in turns with Kampl to break forward, tried his luck from distance just before the 30-minute mark as the away side continued to threaten, but the midfielder's effort was always too high.
Leverkusen remained on the front foot entering the latter stages of the first period, but Atletico were more than happy to sit deep and play on the counter-attack, which made space in the final third extremely difficult to find.
Atletico's best chance of the first half came five minutes before the interval when Antoine Griezmann released Correa inside the Leverkusen box, but Leno was on hand to make a fingertip save, and moments later, the German made an even better stop to keep out Koke's low attempt.
Neither manager looked to their bench at the interval and it was a comfortable start to the second period for Atletico as they took the sting out of Leverkusen's attacking play with a series of comfortable possession.
The visitors did come close to making the breakthrough in the 54th minute when Volland drove into the Atletico box and looked to pick out the far corner, but the forward's effort just missed the post, before Correa sent a similar effort wide of Leno's goal down the other end of the field.
Griezmann was next to come close for the home side just before the hour after Koke had released the Frenchman inside the Leverkusen box, but his chipped effort dropped wide of the far post.
Nico Gaitan for Correa was Atletico's first change of the match in the 65th minute, and the alteration came during a period where both teams were committing players forward in search of the first goal of the night.
Leverkusen had four separate opportunities in the same attack 20 minutes from time as they desperately looked to register, but Oblak made two saves in quick succession to keep out efforts from Brandt and Volland, before Diego Godin cleared off the line and Kampl sent the ball wide of the far post.
Simeone's response to the pressure from Leverkusen was to introduce Stefan Savic in place of Yannick Ferreira Carrasco, meaning that the Spanish outfit switched to a back five for the final 20 minutes of action.
Leverkusen continued to threaten, however, and Oblak had to be at his best to keep out a long-range Karim Bellarabi effort in the 74th minute, before the Atletico stopper prevented a Wendell strike finding the bottom corner five minutes later.
The Bundesliga side continued to press players forward as the match approached its final moments, but Atletico kept their clean sheet intact as the La Liga outfit joined the likes of Barcelona and Real Madrid in the quarter-finals of the competition.