The Foxes were under pressure from the off as Kasper Schmeichel denied Fernando Torres at the front post with four minutes gone, before Koke hammered a 25-yard drive onto the upright just a minute later.
Craig Shakespeare’s men gained a foothold in the game following Atlético’s early dominance and were unfortunate not to have capitalised on a golden opportunity.
Marc Albrighton sent a fizzing cross into Shinji Okazaki, but the delivery was just behind the striker, who couldn’t convert.
Frustratingly, City then fell behind just before the half-hour mark. The recovering Albrighton was deemed to have fouled Antoine Griezmann in the area and the France international dispatched the penalty to fire his side in front.
Opportunities to equalise followed after the break. Robert Huth, who will miss the second leg on Filbert Way after being booked, saw a strike from close range blocked early on in the second period, while Riyad Mahrez curled the rebound over.
But there would be no breakthrough for City, who had to defend resolutely in the late stages to ensure Diego Simeone’s men would not extend their advantage.
Major moment
Much was made about Atlético Madrid’s ability to counter-attack and it was from a swift break that they created their solitary strike.
City lost possession high up the pitch and were punished for it when Marc Albrighton conceded a penalty.
Kasper Schmeichel saved two penalties in the previous tie against Sevilla, but he could to nothing about Antoine Griezmann’s well-taken spot kick.
The goal proved to be the pivotal moment in the match, but Atléti’s lead heading into the second leg is slender.
Who impressed?
On a number of occasions, Wednesday’s hosts pumped the ball into the City box. The Foxes had to deal with Antoine Griezmann free kicks, Koke crosses and Yannick Carrasco deliveries all evening, but deal with them they did.
The man at the centre of defence, alongside the impressive Yohan Benalouane, was Robert Huth, who won countless aerial duels for his side.
He played outstandingly and will certainly be missed when he serves his suspension on Tuesday.
Where do we stand?
The Foxes have been in this position before. A goal down after the first leg against Sevilla, City turned the tie on its head with a convincing win in Leicester.
While they trail 1-0 from the first leg against Atlético, the overall result of the tie remains in Leicester’s hands and with a sold-out Leicester City Stadium behind them on Tuesday, anything could happen.
Coming up…
A trip to Crystal Palace is next for Leicester City, who will now focus on Premier League survival ahead of the second leg of their UEFA Champions League Quarter-Final tie with Atlético Madrid.