Spain strung together a total of 1006 passes to Russia's 290, but much of that was horizontal as the 2010 World Cup champions simply could not find a way past the Russians' Iron Curtain.
But some counter-attacking from Russian Federation late in the half gave paid off, as a Russian Federation corner turned into a penalty thanks to Gerard Pique's flailing arm catching the ball in the air.
Russian Federation will now meet Croatia in the Quarter Final at the Fisht Olympic Stadium, Sochi on Saturday, July 7, 2018. These changes said much about the two teams' ambitions at this point: Russian Federation hanging on for penalties, Spain cursing themselves for still being out there.
Needing to score to keep his side's hopes alive, Iago Aspas sent his effort down the middle, Akinfeev's left foot sent it anywhere but the goal and the 78,000 inside the stadium were sent wild in celebration.
"If you analyse every minute of the match, we had people attacking, we had attackers on the wings, in the middle", Hierro said.
Spain, the 2010 world champions, controlled the game with their slick passing but did little more, failing to create another scoring chance in the first half.
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Spain joined Argentina, Portugal and Germany among the big guns to have been eliminated from this World Cup, but Iniesta said he believed the future for the Spain team was bright. Still, it's hard to see a Kutepov interception making the highlight reel over Akinfeev saving the Iago Aspas spot kick.
Spain stopped Russia's European Championship run in 2008 - the country's best tournament performance since the end of the Soviet Union - and also played to a 3-3 friendly draw a year ago, though one in which Spain didn't field a full-strength team.
The Russians were never expected to sparkle offensively but what was surprising was how sluggish Spain looked when pushing forward.
In the quarterfinals, Croatia will present a different challenge for the host nation, which must make changes. Russia's Alexander Yerokhin went on in the 97th minute against Spain, replacing fellow midfielder Daler Kuzyaev.
Most of that work, of course, was his predecessor Julen Lopetegui's but he was sacked a day before the World Cup began when he revealed that he would be taking over at Real Madrid next season.
Akinfeev claimed Pique's header and pushed away a Rodrigo Moreno shot in extra-time, while the introduction of Aleksandr Erokhin as Russia's fourth substitute made World Cup history.
Gerard Pique smashed Spain's second in off the post, but 38-year-old Sergei Ignashevich wrong-footed David De Gea to equalize.
With Russia withdrawing Dzyuba, the hosts played the last half hour of normal time without anyone left upfield as an outlet, with all 10 outfield players content to sit even deeper as Spain continued their possession domination.