Akinfeev stopped kicks from Koke and Iago Aspas, while Russia's marksmen scored all four penalties they took.
Russian Federation will be now playing in the quarterfinals on July 7 at the Fisht Stadium in the resort city of Sochi against the victor of Croatia-Denmark match, which will be played later in the day.
Spain pushed and prodded as the game moved into this World Cup's first extra-time, but the home defence had its men behind, allowing the ball-players little room to maneuver.
Sergei Ignashevich had unwittingly handed the 2010 champions a 12th-minute lead after tussling with Sergio Ramos, only for Artem Dzyuba to cancel out the own goal with a well-struck penalty (41) after Gerard Pique was punished for handball.
"Years ago, I said he could end up being the world number one".
Spain dominated the ball during the game - completing more than 1,000 passes - but was too passive against a well-organized Russian defense. It was the first match of the tournament to go to penalty kicks. A penalty was the only way they could cause us danger.
Russian Federation introduced Aleksandr Yerokhin for Daler Kuzyayev - the first time ever that a fourth substitute had been used at the World Cup - and Asensio fired straight at Akinfeev from the edge of the area before coming off for Rodrigo as Spain also used their fourth sub.
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Here are the highlights from day 17 at the World Cup...
Besides the penalty kicks in the shootout, there were only a total of seven shots on target at his goal through the tournament, and he conceded goals to six of them, including three to Cristiano Ronaldo.
He added: "We're having a fantastic World Cup".
Akinfeev used his trailing left foot to kick the ball high away from the goal on Spain's last attempt.
The Russia goalkeeper was again involved early in the second half, flying to his left to pluck a spinning Jordi Alba effort from the air.
Spain has had a hard time playing against host nations in the history of the World Cup.
The excitement of the first half dissipated soon after the restart as the game fell into a rather tiresome rhythm of Spain dominating possession without truly threatening.
Spain joined fellow heavyweights Germany and Argentina in making a premature exit, raising questions as to the wisdom of sacking Julen Lopetegui on the eve of the competition.