Julian Alvarez scored a second-half brace as a 10-man Atletico Madrid came from a goal down to beat Bayer Leverkusen 2-1 at home on Tuesday, and take a major step towards a top-eight finish.

Barrios was sent off for a nasty, studs-up challenge after 23 minutes and Leverkusen took advantage as Piero Hincapie put the visitors ahead in first-half stoppage time.

Buoyed on by a fiery 70,000-strong home crowd, Atletico lifted in the second, Alvarez finishing off a length-of-the-field counter to equalise after 52 minutes.

Goalscorer Hincapie picked up a second yellow with 14 minutes remaining and Atletico smelt blood, Alvarez taking advantage of some sloppy Leverkusen defending to score in the 90th minute.

"Things looked bleak," Alvarez said after the match, adding "but by playing our game and staying humble, we got the equaliser.

"Then with 10 against 10, we saw the chance to win."

The last-gasp victory sends Atletico third in the Champions League table, with the top eight sides all avoiding an extra knockout round.

The win means Atletico have already secured last 16 qualification and who travel to Red Bull Salzburg in their final match.

"These are three very important points and they show us to keep believing in what we do," Alvarez said.

German champions Leverkusen, who host lowly Sparta Prague next week, finish the night in sixth.

"We didn't close out the game maturely enough," Leverkusen's Jonathan Tah lamented to DAZN, saying Atletico lured his side into a "fight".

"The stadium pushed them and lifted them high... To lose a difficult away game like that, it hurts extremely badly."

- Red-hot form -

Both sides came into the match in red-hot form. Leverkusen had chalked up 12 straight victories in all competitions while Atletico had 15 wins in a row before Saturday's surprise La Liga loss at lowly Leganes.

Pre-match, both coaches lavished praise on each other.

Atletico's Diego Simeone, who coached his side against Alonso when the Leverkusen boss was playing at Real and Bayern, lauded his opposite number for turning side into an "extraordinary team."

Alonso, who missed Real's 2014 Champions League final win over Atletico with suspension, praised Simeone's "intense and perfect relationship" with his club.

On the pitch however there was no love lost, with the referee handing out four yellow cards and a red in the first half.

Leverkusen were in control before referee Davide Massa changed Barrios' yellow to red after a VAR intervention with 23 minutes gone.

The man advantage supercharged the Germans, who pinned Atletico inside their own area

Leverkusen broke through in first-half stoppage time, Nordi Mukiele lofting a cross for Hincapie to head past Atletico goalie Jan Oblak.

In the second-half, the early control evaporated as both sides played end-to-end, with Atletico using the chaos to equalise.

With Leverkusen on the attack, Antoine Griezmann punted a long pass goalwards, Alvarez forced Tah into a poor clearance, before regathering and guiding a shot into the bottom right.

Leverkusen lost goalscorer Hincapie to a second yellow in the final 15 minutes, prompting Atletico to push higher.

With the visitors failing to deal with a bouncing cross, Alvarez collected the ball and rounded the keeper before converting from a tight angle to snatch a famous comeback victory for the undermanned hosts.