Akinfeev saved spot kicks by Koke and Iago Aspas after both teams had scored two apiece in what was Russia's first World Cuppenalty shootout, to send his team to the last eight after a lacklustre 1-1 draw over 120 minutes.
The hosts will now play the victor of Croatia and Denmark, who play tonight in Nizhny Novgorod. "Great news for us".
The teams having successfully converted two penalties each, Akinfeev saved Spain midfielder Koke's penalty shot, and Russian fans inside a sold-out Luzhniki Stadium gave a loud cheer. He refereed Portugal's 1-0 win over Morocco and Germany's 2-0 loss to South Korea, which eliminated the defending champions.
Russian Federation - the lowest ranked team in the World Cup at No. 70 in the world - is stunningly going to the quarterfinals to face Croatia on Saturday. For Spain, it was another heartbreak at the World Cup.
Spain'sGerard Pique argues against the penalty awarded against him.
A low 20-yard drive heading towards was palmed away by at Akinfeev at full stretch, with the angled follow-up from Aspas also pushed to safety.
"I really had to persuade [my players] that this was the only way out", said the Russian Federation manager, as quoted by the Guardian.
"I'm sure we're going to have a hard time", said Cheryshev. "We left our soul in the pitch". After eleventh hour drama that saw former coach Julen Lopetegui being sacked, the La Roja, under Fernando Hierro, managed to avoid an early exit and even scraped through to the top of Group B table.
As a child, Cheryshev followed his father around Spain from Sporting Gijon to Burgos and then to Real Madrid, where Dmitry Cheryshev coached in the academy and his son learned the game. The 34-year-old Barcelona midfielder came off the bench and nearly won the game with an 85th-minute shot well saved by Akinfeev. But Croatia won the shootout 3-2 after Danijel Subasic saved three spot-kicks.
Spain was more urgent in extra time after being too passive when it dominated the ball in the 90 minutes of regular time.
It was a remarkable finale to a game Spain dominated in terms of possession but simply did not do enough to win and Russian Federation can now look forward to a quarter-final next Saturday in Sochi against Croatia or Denmark.
Dzyuba himself stepped up and sent David De Gea the wrong way. "We believe we will now be in the final with Brazil", said Anna Glazkova, 27, a human relations manager. "That's what we have to believe".
By reaching the round of 16, the hosts were already guaranteed their best World Cup finish in the post-Soviet era.
The king heads FIFA's list of VIP guests for the round of 16 game, which also includes Russia's Prime Minister Dmitry Medvedev.
La Roja's best chance came through Andreas Iniesta, who was a substitute for the first time in the tournament. The limitations of this became obvious when Aleksandr Golovin scampered down the wing in the fourth minute but had nobody to cross to - he held on and settled for a corner.
De Gea made one save at the entire World Cup, and none Sunday when Artyom Dzyuba's 41st-minute penalty was Russia's only shot on target.
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It was the latest in a series of arguments about football and the relative merits of the world's two best players. Portugal had more than 60 percent of possession, which they found hard to translate into a goal.
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