Diego Simeone's side claimed a 4-2 win in the first leg of the last-16 tie in Germany and were never unduly troubled as they produced a composed performance at the Vicente Calderon.
Leverkusen had only beaten Atletico once in their previous five meetings, and although they tested Jan Oblak on a handful of occasions, a stunning comeback rarely looked likely.
Bernd Leno produced two exemplary saves to deny Angel Correa and Koke in the first half, while Antoine Griezmann saw a devilish chip drop just wide, but Atleti chances were scarce in a low-risk performance.
Oblak produced a stunning triple-save to keep the scores level after the imperious Diego Godin was for once beaten, but it proved to be as close as Leverkusen would come to suggesting they could steal a spot in the last eight.
Atleti cruised through the closing stages to secure their spot as the third LaLiga side in the next round, with their attentions now turning to a key league meeting with Sevilla at the Calderon on Sunday.
Atleti looked content to allow Leverkusen to do the early running, but it was not until the 15-minute mark that the first real opportunities for either side arose.
Correa was denied a good chance from close range by a block from Aleksandar Dragovic, and Julian Brandt should have done much better on the resulting counter-attack as he contrived to lose possession when played clean through by Javier Hernandez.
Hernandez fired over the bar with his only sight of goal of the first half as Atleti continued to keep Leverkusen at arm's length, and Leno made two terrific saves to deny Correa and Koke on the break and keep his side in the contest.
Leverkusen missed a good chance to grab a lifeline early in the second half, Kevin Volland dragging a shot wide of Oblak's right-hand post, but Correa was inches from putting the tie to rest after dancing his way into the box from the right before shooting wide.
Griezmann had been quiet for much of the first hour but he almost broke the deadlock in sumptuous style, sending a right-foot chip across Leno's goal and narrowly beyond the far post after springing the offside trap.
Leno had been the busier of the goalkeepers but Oblak produced a moment of brilliance to prevent Leverkusen taking the lead with 22 minutes to play. The Slovenian denied Brandt one-on-one before making two superb reflex saves to deny Volland on the rebound, before Hernandez dragged a shot inches wide.
Hernandez just failed to reach a rebound after Karim Bellarabi brought another save out of Oblak, before Kevin Kampl's precise strike from 25 yards was tipped away from the bottom corner, as Atleti survived a smattering of late pressure to preserve their clean sheet and their place in Friday's quarter-final draw.