He saved Koke's effort to hand Russian Federation the advantage and then, denied Iago Aspas to awaken the subdued 78,000 crowd in Moscow's Luzhniki Stadium.
Russian Federation will now face either Croatia or Denmark in the quarter-final, the first time they have reached the last eight since 1970.
They will face either Croatia or Denmark in the quarter-finals and have every chance of winning if they can put on a defensive performance equal to today's effort and stifle their opponents. He's bound to be a national icon and a hero after the performance of his life, and it's also one of the biggest upsets we've seen in Cup history when it comes to Federation Internationale de Football Association rankings.
12' GOAL! Spain 1-0 Russia: Spain have taken the lead!
Meanwhile, Spain's rotten run against host nations at major tournaments continues.
Following the loss Iniesta said to the reporters: "It's a reality that is my last game with the national team".
Spain, buoyed by their breakthrough, were beginning to dominate possession with Russian Federation struggling to find a foothold, but the hosts were briefly boosted when an Dzyuba header from a long free kick caused confusion before Spain whacked it clear.
Answering a question from RT Sport in the press conference after the game on his emotions following such an historic win, Russian Federation manager Cherchesov said he is concentrating only on the next game, despite the gravity of the result.
Spain, who parted ways with coach Julen Lopetegui just days before the tournament, joined England and Italy as the only teams to lose three shootouts at the World Cup, having been knocked out by hosts South Korea in 2002 and Belgium in 1986, both in the quarterfinals.
Everyone inside the Luzhniki Stadium, and all those watching at home, held their breath as the referee and the VAR team checked footage for holding on Gerard Pique and Sergio Ramos late on in extra time.
Mighty Spain dominated the field at Luzhniki Stadium, dulled the senses with mind-numbing ball movement around the perimeter of the penalty area Sunday.
As the Iberians grew desperate, trying a more direct approach to goal, Iniesta came close - collecting a chested pass from the fellow second-half substitute Iago Aspas - but a diving Akinfeev brilliantly turned away his snapshot from outside the box. Iniesta close to giving what would have surely been the victor for Spain. He smiled just before Akinfeev saved the shot with his trailing leg.
Akinfeev denied two Spanish shots in the shootout, but the last one was his best.