After Alexander Sorloth and Julian Alvarez missed from the spot for Diego Simeone’s Atletico, Pablo Marin smashed home his kick to claim victory for the Basque side.
Ander Barrenetxea had headed Real Sociedad ahead after just 14 seconds, with Ademola Lookman levelling for Atletico.
Mikel Oyarzabal put the Basque side ahead from the penalty spot before the break but Alvarez rescued Atletico and forced extra time and ultimately penalties with a superb strike.
La Real’s season seemed set to be one of struggle until American coach Pellegrino Matarazzo was appointed in December, and he resuscitated their campaign.
“It’s a moment to enjoy, to dream and to believe… the kid who dreamed of this… has done it,” said Real Sociedad goalkeeper Unai Marrero, who saved two penalties.
Champions League semi-finalists Atletico, 10-time winners of the cup, were left to lick their wounds and rue mistakes.
“We did everything we could, we had to row against the current from the start,” said Atletico captain Koke.
“We had some chances before the end of the 90 minutes that if we had scored would have changed the story.
“We have to congratulate La Real, that’s life. It hurts but we have to continue.”
At La Cartuja stadium it was a battle between two teams that often attack fast and direct, and Real Sociedad certainly did that, netting the quickest ever goal scored in a Copa del Rey final.
Goncalo Guedes scampered away down the left on to a long ball, crossing for Barrenetxea to head beyond Juan Musso before the Rojiblancos had even touched the ball.
Simeone’s side, who last won the competition back in 2013 near the start of his 14-year reign, wrestled their way back level through Lookman.
Antoine Griezmann laid off the ball to him on the edge of the box and without much on, the Nigeria international spied a route to goal and drilled into the bottom corner.
Lookman almost created a goal for Griezmann, but Real Sociedad scrambled to block the 35-year-old French forward, who is leaving Atletico at the end of the season for MLS side Orlando City.
Atletico goalkeeper Musso, chosen ahead of the fit-again Jan Oblak after he impressed during the Slovenian’s recent injury absence, handed La Real the lead again just before the break.
Musso clumsily clattered Guedes fists first as the Portuguese leapt for a header and the Basque side were awarded a penalty.
Oyarzabal, who scored from the spot when they won the 2020 edition, without their fans present because of the global pandemic, sent Musso the wrong way.
After a first half in which they struggled, Atletico began to build some pressure after the interval.
Griezmann lashed over and Lookman whipped a shot high and wide as La Real tried to stave off the Rojiblancos, who dominated the ball.
Simeone called for his battering ram, sending on Norwegian target man Sorloth to try and force a way through.
Eventually the goal they craved came from the guile of former Manchester City striker Alvarez instead.
The Argentina forward took a neat touch to spin on the edge of the box and then another to plant the ball in the top corner for his 19th goal of the season.
With La Real caving Johnny Cardoso should have won it for Atletico in stoppage time. The American fired a golden opening wide of the far post with just goalkeeper Unai Marrero to beat.
Musso made a fine save to thwart Icelandic striker Orri Oskarsson as he tried to turn home a rebound in extra time.
At the other end Alvarez crashed a shot off the crossbar from long range, with both teams creating enough opportunities to win it before penalties.
Marrero denied both Sorloth and Alvarez on Atletico’s first two penalties, with Musso stopping one from Oskarsson to give Atletico a chance.
However Marin made no mistake with Real Sociedad’s fifth penalty to spark wild celebrations.
Atletico’s last realistic chance of silverware this season, and something for Griezmann to celebrate on his departure, is in Europe where they face Arsenal.
“We have a beautiful challenge — we want the Champions League, we will do everything we can to win it, but this is a sad night,” added Koke.
