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.

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.

Atletico seemed likely to end a history of being dominated by Madrid in Europe but Los Blancos have the knack of survival down to a fine art and took the game to penalties.

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

Marcos Llorente also missed for Atletico and Madrid's Antonio Rudiger struck the winner for the reigning champions.

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.

They 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.

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.

With a strong hand Courtois batted away a powerful Alvarez effort as Atletico sought a second, then denied the Argentine again at his near post before half-time.

The Belgian goalkeeper made another save to deny Alvarez soon after the break too, as Atletico continued to threaten and Jan Oblak was still untested.

- High tension -

With Atletico controlling the game, Ancelotti brought on Eduardo Camavinga and Lucas Vazquez in search of fresh energy.

Madrid soon produced their best attack of the game, with superstar trio Vinicius, Jude Bellingham and Kylian Mbappe combining on a rapid counter.

Mbappe skipped away from Jose Gimenez and then was dragged down by the desperate Clement Lenglet for a penalty before he could shoot.

After the French forward missed spot-kicks against Liverpool and Athletic Bilbao earlier in the season, Ancelotti said Vinicius was his team's primary taker.

So it was the Brazilian forward who stepped up, facing down a red wall of whistling Atletico fans behind the goal, and buckled under the pressure, firing high and wide of the target.

Correa almost snatched Atletico victory in the last minute but hammered a vicious half-volley over the crossbar, and the match went to extra time.

Madrid shaded the additional period as both teams looked tired but pushed themselves to their limits with the match on a knife-edge.

Mbappe stepped up first from the spot and sent Oblak the wrong way, with Bellingham following suit after Alexander Sorloth netted for Atletico.

Alvarez slipped as he smashed home the hosts' second penalty and after a VAR review it was ruled out as he had touched the ball twice as he struck it.

Oblak saved from Vazquez's weak penalty to put Atletico back on track but it was short-lived as Llorente crashed his penalty off the bar.

Oblak dived the right way for Rudiger's decisive penalty but could not keep it out as Madrid marched into the last eight, where they will take on Arsenal.