The game started rapidly when Mikel Oyarzabal was felled by Jan Paul van Hecke in the area, and the Real Sociedad forward fired home from the spot.
That wasn't the case after half-time. Robin Le Normand was adjudged to have brought Memphis Depay down moments after the restart, and the ex-Manchester United man lashed home to level. Oyarzabal grabbed his second with a header.
Debutant star Ian Maatsen didn't read the script though, as he lashed home to level at the Estadio Mestalla - sending the game to extra time. Lamine Yamal left his mark with a superb chop and curled finish - but after the extra-time interval, substitute Xavi Simons equalised by penalty for the third time, sending the game to shoot-outs.
Donyell Malen was the villain, missing his spot-kick while Pedri smashed home the winner in sudden death - and it's Spain who are into the semi-finals.