Aspas' penalty kick is saved and the hosts are through to the quarter-finals of the World Cup.
They though they had penalty with five minutes left in the match, with Pique seemingly pulled down in the area. It was the first match of the tournament to go to penalty kicks.
La Roja took the lead through Sergey Ignashevich's own goal after just 11 minutes.
Their match against Spain didn't exactly get off to a dream start.
With five minutes to go they were agonisingly close to a victor as Iniesta latched on to a clever touch from Aspas and his low strike from the edge of the area hit the post.
But despite recording 78.2 per cent possession in Moscow, Spain could not find a way to break down Russian Federation as the tie entered extra time.
Having long run out of steam and with several players cramping, Russian Federation were reduced to desperately defending in extra time.
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As of now, there is little proof that North Korea intends to go down that road, longtime North Korea observers say. Meeting with Kim Jong Un was an interesting and very positive experience.
Considering their turbulent start to the FIFA World Cup, Spain will be pleased to have safely negotiated the group phase, even if they are yet to click under interim head coach Fernando Hierro.
Koke had his penalty saved early in the shootout, giving Russian Federation the advantage, and then Igor Akinfeev saved Iago Aspas' spot kick with his foot to send his side into the last eight and send Spain home from the tournament.
Aspas was unable to get the ball under control after Iniesta had threaded a pass through into the area, with Spain pinning Russian Federation deep inside their own half but still unable to find a way through.
Everyone inside the Luzhniki Stadium, and all those watching at home, held their breath as the referee and the VAR team checked footage for holding on Gerard Pique and Sergio Ramos late on in extra time.
Despite the added time of two minutes, both times retreated for the 15-minute break with the scoreboard flashing 1-1.
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 Denmark or Croatia, after a lackluster 1-1 draw over 120 minutes.
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