Saul Niguez gave the visitors the lead with a stunning strike, picking the ball up on the right side before cutting inside and curling a left-footed shot into the top corner.
Antoine Griezmann doubled their away goal advantage from Kevin Gameiro’s assist after woeful defending by Leverkusen captain, Omer Toprak.
Wendell struck his own crossbar while trying to clear Felipe Luis’ cross and the goalkeeper Bernd Leno twice saved well from Griezmann as Leverkusen were fortunate to go in at the break lagging by just two goals.
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Karim Bellarabi pulled one back for Leverkusen early in the second half by finishing off a quick and smooth team play, but Gameiro’s penalty restored Atletico’s two-goal advantage before Stefan Savic’s own goal reduced debts once again.
Substitute Fernando Torres further strengthened Atletico’s grip on the fixture when he nodded in a late fourth goal.
The return leg takes place at the Vicente Calderon on Wednesday, 15 March.