Koke and Iago Aspas were denied by the Russia goalkeeper as 2010 champion Spain, which dominated possession without creating clear chances, was defeated 4-3 on penalties.
Sergei Ignashevich became the oldest scorer of an own goal in FIFA World Cup history when the 38-year-old gave Spain an early lead at the Luzhniki Stadium.
A right-wing Isco cross isolated Ignashevich and Sergio Ramos at the back post, the Russia defender turning the ball home via his heel as he desperately tried to block his opponent's run.
But Russia drew level in the 41st minute, Artem Dzyuba smashing home a penalty after his header was blocked by Gerard Pique's arm in the box.
A stodgy Spain could not break the host down and was denied a penalty after a VAR review in extra-time, sending the tie to a shoot-out.
Akinfeev saved a terrible Koke penalty to put Russia in control and with David de Gea unable to stop any of the four kicks he faced, Aspas' effort was brilliantly blocked by the goalkeeper to spark chaotic celebrations.