Two lethal counter-attacks in the opening 25 minutes put the 2014 and 2016 finalists in the driving seat, with Saul Niguez and Antoine Griezmann on target, and gave them the edge for a quarter-final spot for the ninth time.
"We knew it was going to be a tough game. We wanted to win, we did that and the return leg will be as difficult as tonight was," said Griezmann.
"They pressured us and made life difficult but the boss's changes helped us win the game tonight. We have a big game to play now in front of our own fans."
Leverkusen, who paid the price for a disastrous defensive performance, cut the deficit before Atletico's Kevin Gameiro scored with a spot kick and Stefan Savic's own goal set up a nervous finale.
Substitute Fernando Torres ended any speculation with his goal in the 86th minute to take revenge for last season's 1-0 loss as the Germans suffered their first home defeat in Europe after a 10-match unbeaten run.
"It is easy to see how Atletico have reached two finals in three years," said Leverkusen coach Roger Schmidt. "We knew of their counter-attacking abilities before the game but we ended up shipping two goals in the first half."
The Bundesliga club, finalists in 2002 before the introduction of the round of 16, are now at risk of missing out on the last eight for the fifth time, having never gone past this stage on their four previous attempts.
They were supposed to be dangerous on the break but it was Atletico who came close early on with keeper Bernd Leno stopping a Griezmann effort and Wendell seeing his subsequent clearance bounce off his keeper's crossbar.
Niguez did better in the 17th minute, charging down the right and curling his shot past Leno after it took a slight deflection off Aleksandar Dragovic.
Griezmann then doubled the score after the hapless Dragovic fluffed his clearance and sent the ball into the path of Gameiro who picked out the onrushing Frenchman.
Leverkusen played completely into Atletico's hands with their high defensive line, for the first time in this season's competition conceding goals in the opening 30 minutes.
Griezmann should have added another in the 34th when Gameiro again sent him through but Leno stood his ground and the hosts cut the deficit three minutes after the restart with Karim Bellarabi from inside the box.
But their hopes were short-lived as Dragovic capped his nightmarish performance by giving away a penalty after bringing down Gameiro.
Savic's own goal put Leverkusen back in the game but despite constant pressure they failed to carve out an equaliser before Torres finished them off.
(Reporting by Karolos Grohmann; Editing by Clare Fallon)
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