Real Madrid produced a gritty display to reach the Champions League quarter-finals with a 4-2 win on penalties against rivals Atletico Madrid, following a 1-0 defeat after extra time on Wednesday.

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Diego Simeone's side outplayed the record 15-time champions at the Metropolitano stadium for much of the game, but Madrid have never been eliminated by Atletico in the competition and they battled hard after Conor Gallagher's first-minute opener to secure a 2-2 aggregate draw.

Thibaut Courtois made several saves to thwart Julian Alvarez and Vinicius Junior blazed a penalty high and wide for Madrid.

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In the shoot-out Alvarez scored for Atletico but his effort was controversially ruled out for seeming to touch the ball twice because of a slip as he shot.

"The ball didn't move," complained Simeone. "I want to believe they saw he touched it (twice)."

Marcos Llorente also missed for Atletico and Madrid's Antonio Rudiger struck the winner for the reigning champions, who will face Arsenal in the last eight.

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"I had to pick the coldest players possible (for penalties)," said Real coach Carlo Ancelotti. "I think it's a lottery still, a toss-up, today it came in for us -- Atletico go out with their heads held high because they played at a good level."

Atletico played with caution in the first leg despite trailing, willing to take a single goal deficit back to the fiery Metropolitano stadium, where they believed they could really turn the heat up on their arch-rivals.

Real Madrid knocked Atletico out in the 2017 semi-finals in the final European game at the Vicente Calderon, with this the first time the derby has been played at Atletico's new home in the Champions League.

After defeats by Madrid in the 2014 and 2016 finals, the latter on penalties, and elimination on every other occasion the teams have met in the competition, Atletico were desperate to change the narrative, but came up fractionally short.

"I think we played a great match, but unfortunately we lacked a bit of luck," Atletico goalkeeper Jan Oblak told Movistar. "The truth is that one feels pain, it hurts a lot."

Atletico came flying out of the blocks and took the lead after just 27 seconds through Gallagher, levelling the tie on aggregate.

Rodrigo De Paul's low ball in from the right was not cut out by Raul Asencio and former Chelsea midfielder Gallagher lunged in to beat Courtois from close range.

"We came out as if it was already won and in the first move they scored a goal against us, and that messed us up a lot," Madrid midfielder Fede Valverde told Movistar.

Atletico were content to sit deep and soak up pressure as Real Madrid pushed the ball around in their territory but were also ready to spring forward on the counter.

Courtois saved on three occasions from Alvarez, who had scored a brilliant goal in the first leg.

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