Antonio Rudiger's header with five minutes remaining in extra time qualified Real Madrid for the final of the Copa del Rey on Wednesday night after it was made to work harder than expected for a 4-4 draw and 5-4 on aggregate.

Real Madrid may have expected a relatively comfortable passage to the final after winning the first leg of the semifinal 1-0 in San Sebastian, but Real Sociedad produced a heroic display on the night and was minutes from causing an upset.

After Endrick had sent an overhead kick just wide of the post, Real Sociedad took control of the game in midfield and opened the scoring in the 16th minute when a long move ended with Mikel Oyarzabal flicking the ball to Ander Barrenetxea, who advanced into the Madrid area and scored with a low shot between goalkeeper Andriy Lunin's legs.

The visiting team had a setback soon afterwards when defender Nayef Aguerd went down with a calf injury and was replaced with Aritz Elustondo.

Endrick leveled for Madrid after half an hour, latching onto Vinicius' pass and dinking the ball over goalkeeper Alex Remiro after breaking the visitor's offside trap.

Madrid controlled much of the ball for the rest of the first half, but after the break the visiting team again stepped forward and got its reward when David Alaba deflected Pablo Marin's close-range cross into his own net in the 72nd minute.

Eight minutes later, Takefusa Kubo's run set up Oyarzabal to make it 3-1 for the visitor and for a moment it looked as if an upset was on the cards.

It was only a brief moment after Vinicius turned Hamari Traore to set up Jude Bellingham to make it 3-2 and level the score on aggregate, and when Aurelien Tchouameni headed in a corner in the 86th minute, it looked as if it was job done for Real Madrid.

However, a bad foul from Eduardo Camavinga in injury time gave Real Sociedad a free kick on the edge of the Madrid penalty area. Sergio Gomez's delivery was perfect and an unmarked Oyarzabal headed into the net to force extra time.

Madrid had the better of the first period, but the closest either side came to scoring was a Kylian Mbappe chance that was hustled out of play, but after Rudiger's header Real Sociedad had nothing in their legs to produce another miracle.