Antoine Griezmann was given an opportunity to double his side's lead from the penalty spot with five minutes of normal time remaining, but he ended up clattering the ball off the crossbar.
It was an interesting tactical battle between the two teams as it was a cagey start, with Atletico seemingly content to play on the counter-attack.
An early goalscoring chance fell to Fernando Torres when he was gifted the ball in the final third after Javi Martinez's heavy touch, but the striker could not get a shot away as his opponent atoned for his mistake with a tackle.
Bayern had spells of possession, but they looked in trouble at times in defence, particularly when chances fell to Torres and Carrasco, who dropped his shoulder before unleashing a shot from the corner of the box.
Manuel Neuer punched the ball clear, but the Bayern goalkeeper was nowhere in sight when Torres got on the end of a corner, only to direct his close-range header onto the post.
Atletico eventually took the lead in the 35th minute when Carrasco broke away from his marker before drilling the ball low and hard into the bottom corner.
Franck Ribery had the chance to score an instant equaliser at the other end when the ball dropped to him in the box, but the Frenchman opted against striking first time and sent the ball wide.
After the break, Muller was given a sniff at goal when the ball was delivered deep to the far post from the corner flag, but the attacker could only direct his header into the side-netting.
David Alaba tried to make things happen for his team by edging into the box before unleashing a left-footed shot towards the top corner, but it was comfortably parried away by Oblak.
Saul Niguez tried to go for glory with a long-range effort, but it did little to trouble Neuer as Atletico looked relatively comfortable as the clock ticked along.
Bayern knocked on the door, but their competitors were as stern as ever in defence, preventing the Bundesliga giants from finding a way through.
Atletico still posed a threat at the other end, and Carrasco came close to scoring a second goal by cutting inside on his right foot before aiming the ball towards the far corner.
Neuer had to scramble across his goal to meet it, but he managed to get a hand on the ball to push it away from danger.
Lewandowski squandered an opportunity late in the game as the ball was lofted high into the box, but the striker's close-range header ended up glancing inches wide of the post.
Overall, it was a frustrating night for Bayern as they failed to find an equaliser, which drops them three points below Atletico in the group, while PSV Eindhoven and Rostov are two behind.