Highlights: Spain 1-1 Russia (3-4 pens)
Russia received the backing of president Vladimir Putin before their World Cup last-16 victory over Spain.
Putin called Russia boss Stanislav Cherchesov before the hosts defeated the 2010 champions on penalties.
"Before the match, around noon, the president called the coach and wished him well," said Kremlin spokesman Dmitry Peskov.
Putin did not attend the match in Moscow and it is not known if he will attend Russia's quarter-final.
Russia have reached the last eight despite having a world ranking of 70, the lowest in the tournament.
They progressed from their group through victories over Saudi Arabia and Egypt, then held Spain to 1-1 after extra-time, prevailing 4-3 in the shootout.
Peskov added: "Putin said that under Cherchesov's leadership, our guys have already accomplished the impossible - made it out of the group.
"Putin also noted that regardless of the outcome of the match against Spain, no one in our country was going to judge them."
Russia will meet Croatia or Denmark in the last eight in Sochi on Saturday.
Source: bbc.com