An early Sergei Ignashevich own goal had Spain on track to reach the quarter-finals, but Artem Dzyuba levelled from the penalty spot.
Argentina held the previous record of 703 successful passes in a FIFA World Cup match against Greece in 2010, although Opta has only collected this data since 1966.
Spain's 779 passes smashed that record but they were unable to break the determined hosts down at the Luzhniki Stadium.
Captain Sergio Ramos attempted 150 passes over the 90 minutes, followed by Koke's 127, with Isco and Jordi Alba also passing three figures.
But despite recording 78.2 per cent possession in Moscow, Spain could not find a way to break down Russia as the tie entered extra time.