The 32-year-old keeper saved Koke's and Iago Aspas' spot kicks after both teams had scored two apiece in Russia's first ever World Cup penalty shootout, to set up a last eight clash with either Croatia, who also edged out Denmark in a penalty shootout later on Sunday.
"Players will not do things just because the coach says so".
After Artem Dzyuba's penalty had cancelled out the own goal from Sergei Ignashevich that opened the scoring, Russian Federation spent most of the game on the defensive, maintaining a rigid structure that Spain's tiki-taka was powerless to penetrate.
A defensive error let Russian Federation level in the 41st, after Gerard Pique's raised arm blocked a header by Artyom Dzyuba.
The teams meet at the Luzhniki Stadium on Sunday for a place in the quarterfinals, but Russia's progress even to this stage something of a surprise after most pre-tournament predictions viewed them as candidates to exit in the first round.More news: England v Colombia LIVE in pictures
After the match, hero-goalkeeper Akinfeev said Russia's game plan all along had been to hold on for a penalty shootout.
Russian Federation extended a streak of World Cup hosts winning penalty shootouts to five.
Stretching every part of his body out into a star shape and diving to his right, Igor Akinfeev flicked out his left foot and kicked the ball high away from danger.
At the other end, concerns remain about their backline despite the presence of two of the best central defenders in Sergio Ramos and Gerard Pique.
Spain has had a hard time playing against host nations in the history of the World Cup.
Forward Artem Dzyuba buried it for his third goal of the tournament, to equalise and awaken the subdued crowd.More news: Australias Finch smashes own record for highest T20I score
"The Spanish squad is a very outstanding team, which play in a total control of the ball", Samedov said.
After a long period of Spanish possession, Dzyuba finally won a header to give Russian Federation its first sight of goal from which Golovin failed to hit the target.
"We're insanely happy", Dzyuba said.
Despite 75 percent possession, Spain's famed tiki-taka passing game rarely carried them into the box and they had to wait until the 85th minute to test Akinfeev with a low drive from substitute Andres Iniesta. "We won against them - nobody believed we could, but we did".
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.
World Cup history was made with the first use of a fourth substitute, which Federation Internationale de Football Association now allows teams in extra time.More news: Thunder are angling for seven more seasons of Paul George
Denis Cheryshev was born in Russian Federation but spent most of his life in Spain because his father Dmitry, also a professional player, played and coached at several clubs in the country.