Ramos confidently stroked his spot-kick home before Denis Cheryshev put pressure on Iago Aspas.
Sid Lowe's match report from the Luzhniki Stadium will follow.
Aspas almost picked out Carvajal with a cut-back seconds into the start of extra time, which saw Aleksandr Erokhin come on as Russia´s fourth sub - the first time the rule has been applied at the World Cup. Russian Federation will return to the Luzhniki Stadium, having played their opening match at the iconic venue, and will lean on fervent support to go in search of a famous win.
At this point, Spain had not had a shot on goal but twice in added-on time, Diego Costa attempted to regain his side's advantage, only to see a shot from an acute angle and a header saved by Igor Akinfeev.
After changing managers on the eve of the tournament, Spain has played well for spells under Fernando Hierro but has also looked vulnerable at times, and Russian Federation will look to pounce, buoyed by the home crowd.
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.
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And their resolute defensive display continued into extra-time as Isco and co. failed to find a breakthrough.
However, Iniesta's effort was parried away by Igor Akinfeev and extra time was called in Moscow.
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.
Akinfeev came to the rescue again to deny Rodrigo after his fine sprint in the second half of extra time before becoming a national hero by saving the two spot kicks to send the hosts past the former world champions. But after consulting VAR the referee ruled out a penalty.
Despite a centre-back pairing of Sergio Ramos and Gerard Pique, Spain have conceded five goals in three games with goalkeeper David de Gea looking a shadow of his usual self.
"We are having a fantastic World Cup", said Akinfeev.