Leverkusen were gunning for revenge after their European elimination at the hands of Atleti in 2014-15, and they had every reason to be confident following an eight-game unbeaten run in the Champions League, with only Real Madrid on a longer streak.
However, the visitors made an electric start, Saul Niguez and Antoine Griezmann putting them two goals up at half-time, before Karim Bellarabi pulled one back early in the second half.
Stefan Savic's own-goal after a Kevin Gameiro penalty prompted a late onslaught from Leverkusen, but Atleti were always dangerous on the break and Fernando Torres' late header restored their two-goal cushion.
A heavy home defeat leaves Leverkusen's chances of progression hanging by a thread in an underwhelming season that has seen head coach Roger Schmidt fight off reports that he could be sacked.
Diego Simeone's side have also struggled to replicate their best form this term, and their new-found defensive frailties were on display again, but a scintillating attacking display bodes well for the weekend's clash with Barcelona.
Atletico immediately pinned Leverkusen back in their half from the off and came close to opening the scoring twice in rapid succession after just 12 minutes.
Griezmann first called goalkeeper Bernd Leno into action with a low show from a narrow angle, before Wendell hit his own crossbar moments later with a clumsy clearance after Filipe Luis' cross from the left.
There was no such escape for the hosts five minutes later, however, as Saul handed Atletico the lead with a stunning strike, cutting inside onto his favoured left foot and curling a beautiful shot into the top corner past the helpless Leno.
Things went from bad to worse for Leverkusen as Aleksandar Dragovic inadvertently sent Gameiro on his way with a poor clearance on the halfway line and the Frenchman raced clear before setting up Griezmann for a composed finish inside the box.
Griezmann should have made it three following more good work from Gameiro after yet another rapid counter-attack, but Leno pulled off a sharp save to deny him.
Leverkusen seemed emboldened by that life and Bellarabi gave them hope when he pounced on Benjamin Henrichs's low cross from the right and beat goalkeeper Miguel Angel Moya with a clever finish in the far corner.
Gameiro rattled the crossbar soon after as Leverkusen's vulnerability on the break was laid bare and the France striker had his goal in the 58th minute - slamming home from the penalty spot after he was hauled to the floor by Dragovic.
Again Schmidt's side were back in the contest when Moya could only palm a cross into Savic's shins and the ball bobbled home, but Leverkusen's desperation to level the tie would ultimately cost them.
Torres dealt Leverkusen a hammer blow with five minutes left on the clock, heading smartly across Leno and in from a sublime Sime Vrsaljko cross to give last season's runners-up control of this tie.