Karim Benzema and Vinicius Junior's extra-time strikes earned Real Madrid a 3-1 win over rivals Atletico Madrid on Thursday to reach the Copa del Rey semi-finals.

The Brazilian winger's goal was a particularly sweet one for him after a crude effigy with his shirt on was hung from a bridge near Real Madrid's training ground before the game.

The spiky, gripping derby clash turned against Diego Simeone's side in the additional period when defender Stefan Savic was sent off.

Atletico took the lead through Alvaro Morata after 19 minutes but Rodrygo's sensational slalom run past three defenders and slick finish pulled Madrid level with 11 minutes remaining.

After Savic's 99th minute red card, Benzema tucked home from Marco Asensio's pass and Vinicius netted at the death to send Los Blancos through to the final four for the first time since 2019.

"Today we had a very difficult game but with the character and the players that we have, we were able to turn it around," Benzema told Teledeporte.

"Suffering is not good -- we have to score the goals earlier."

The build-up to the derby was tainted by the Vinicius effigy being strung up overnight, which the club described as "a disgusting act of racism, xenophobia and hatred."

"(Vinicius) really wanted to play and he had a very good game," Madrid coach Carlo Ancelotti told a news conference.

"I think the goal was his reward for his great work. What happened is very regrettable."

Madrid fans had planned to sing Vinicius' name in support in the 20th minute, matching his shirt number, but were stunned into silence by Morata's goal moments before.

Atletico, hitting their best form of the season, conjured a brilliant move to break the deadlock, with Morata tapping home after Koke's dink allowed Nahuel Molina to stroke a first-time cross to the back post.

Madrid added another name to a long injury list when Ferland Mendy had to be replaced before half-time, with Eduardo Camavinga slotting in at left back and Dani Ceballos coming on.

Madrid improved significantly after the break and Rodrygo levelled with 11 minutes to go with his jinking solo effort and subtle near-post finish, taking the clash to extra-time.

Atletico defender Savic foolishly handed Madrid the edge when he was sent off for two yellow cards in two minutes.

Atletico players claimed that Ceballos should have been sent off earlier when he fouled Geoffrey Kondogbia while on a yellow card.

"I think it was a red (for Savic), but they should have had one too when we were 1-0 up," complained Atletico goalkeeper Oblak.

"They could have had a second yellow but (the referee) decided it how he decided, we are used to that, and it's complicated, but the team fought to the end, we did everything to score."

With an extra man Madrid capitalised, Benzema striking lethally after 104 minutes when Vinicius miskicked Marco Asensio's cross and the ball travelled through to the striker.

Madrid, who last won the Copa del Rey in 2014, kept Atletico at bay in the final 15 minutes before Vinicius dribbled through and fired home to clinch the victory -- celebrating with a now customary dance routine.

Despite their improving performances, the rest of Atletico's season is looking barren, given they were eliminated from European football and are 13 points behind La Liga leaders Barcelona, having played a game more.

"We are out of Europe and now the cup, the team has the second half of the season ahead of them to try and qualify for the Champions League, that's the objective the club needs," said Simeone, who cast some doubt on his future.

The Argentine coach has been at the club since 2011 and has a contract until 2024.

"After that, calmly, we will look at what is convenient for everyone," he continued.

"Being at Atletico gives me enormous joy, I will give 1000 percent until the day that I leave."

Earlier Athletic Bilbao won 3-1 at Valencia to join record 31-time winners Barcelona and Osasuna in Monday's semi-final draw. (AFP)