Forward Artem Dzyuba buried the 41st-minute penalty for his third goal of the tournament, sending Spain keeper David de Gea the wrong way to equalise and awaken the subdued crowd.
"Everything is changing, " Spain coach Fernando Hierro said through a translator.
Dzyuba's header off a corner hit Gerard Pique's arm and the striker converted the spot-kick that he had earned.
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.
The 34-year-old, who scored the winning goal at the 2010 World Cup final, won 133 caps in an global career spanning 12 years, during which he also won European championship titles in 2008 and 2012.
"We are playing at home but I think the team is relaxed and very much ready to do a good job".
Russia's defender Ilja Kutepov (centre) vies with Spain's midfielder Isco during their 2018 World Cup round of 16 match at the Luzhniki Stadium in Moscow on July 1, 2018.More news: Cavani the hero as Uruguay sink Portugal
Russian Federation are hoping for a World Cup miracle on Sunday as the host nation take on 2010 winners Spain for a place in the quarter-finals after Cristiano Ronaldo and Lionel Messi exited the tournament.
"I just feel emptied out", Akinfeev said.
Despite being heavy favourites to beat Russia, Spain lined-up with two holding midfielders in Koke and Sergio Busquests, while Andres Iniesta was left on the bench.
Having long run out of steam and with several players cramping, Russian Federation were reduced to desperately defending in extra time. "The fact that the game will be at Luzhniki Stadium with nearly 80,000 people supporting us is probably the only good outcome from the fact we finished second in our group", said Ignashevich.
But the Spaniards just seem to revert to their pre-2008 frustrating selves - full of ability but no end product as they kept up a freakish record of nine losses to World Cup and European Championship hosts since 1934.
Spain join Germany, Argentina and Portugal as the fancied teams eliminated.
Charged with giving false testimony for his role in a corruption case that saw former Dinamo Zagreb chief Zdravko Mamic sentenced to six-and-a-half years in prison last month, Modric's popularity has dipped despite continued brilliance on the field for his club Real Madrid and country. "But any team can hurt another and we'll certainly do our best".
Akinfeev came to the rescue once again to deny Rodrigo after his fine sprint before becoming a national hero by saving the two spot kicks to send the hosts into the last eight and his fellow Russians to the streets to celebrate. Pique, Ramos, David Silva, Costa and Sergio Busquets will be 33 or older.