An own goal from Sergei Ignashevich early on gave La Roja the advantage against the hosts.
Fernando Hierro's men, however, were pegged back by an Artem Dzyuba penalty when Gerard Pique handled in the area to tie the game at 1-1, a result that stood until full time.
Spain failed to create clear-cut chances against a resolute Russia backline despite enjoying almost total domination in possession.
Indeed, they set a new World Cup record with an incredible passing rate over the first 90 minutes.
Hierro's men completed a total of 770 passes before extra time, the most ever in a World Cup match since records began.
Argentina had held the previous record, having made 703 against Greece in a 2010 group stage clash.
Including extra time, Spain passed the 1000-pass milestone, the first team ever to do so.
Real Madrid defender Sergio Ramos, who helped force Ignashevich's own goal, was the fulcrum of Spain's passing game carrying the ball out from the back.
Ramos made a whopping 141 passes, the most of any World Cup player since records began.