Akinfeev had already made good saves as Russian Federation held on to force extra-time and spot-kicks - but he then saved from Koke and Iago Aspas in the shoot-out.
Rewarded with a sponsor's trophy, Akinfeev acknowledged the part played by an 78,000 crowd in Moscow: "I'm not the man of the match, the man of the match is our team - and our fans".
Spain was cautious to the extreme, passing the ball more than 1,029 times successfully, but rarely near the Russian goal.
Russian Federation will now meet Croatia in the Quarter Final at the Fisht Olympic Stadium, Sochi on Saturday, July 7, 2018.
Akinfeev says, "We were hoping for penalties because Spain are hard to beat - Spain can't always be lucky".
The teams started the match quite relaxed.
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A total of 32 national football teams entered the 2018 FIFA World Cup and only 16 of them proceeded to the knockout phase after the group stage, which kicked off on June 14 and ended on June 28. Home supporters with red-white-and-blue wigs and painted faces seemed prepared for an unhappy ending out of Tolstoy or Dostoyevsky, especially after Marco Asensio's free kick ricocheted off a calf of defender Sergei Ignashevich in the 12th minute and past goalkeeper Igor Akinfeev for an own goal.
Croatia reached the quarterfinals just like Russian Federation - on penalties after a 1-1 draw - but its win over Denmark was a very different game, and its style could hurt Russian Federation in Sochi on Saturday.
The second half saw no change even though Cherchesov appeared to get a little more adventurous by bringing on three-goal scorer Cheryshev on the hour.
After 120 minutes of football and with the teams tied 1-1, referee Bjorn Kuipers from the Netherlands whistled for penalties.
With several players cramping, Russian Federation were reduced to desperately defending in extra time as Spain, who played more than four times the number of passes their opponents did, still struggled to create clear chances.
Before the game, he had compared Russia's qualification from the group stage to a fairy tale, and the fans echoed that with a vast banner reading: "You were born to make the fairy tale real".
Stanislav Cherchesov said that his tactics - and the way his players executed them - were the key to Russia's surprise last 16 victory over Spain. And frankly, had the ball not gone in, Spain might have been given a penalty for what looked like a foul. A win for Russian Federation would open up the competition on their side of the draw. Koke tried to give the lead back to Spain but his shot was stopped by Akinfeev.