Russia beat Spain on penalties at Moscow's Luzhniki Stadium and reached the quarter-finals for the first time since the break-up of the Soviet Union in 1991.

"The total number of those who partied in the center of Moscow is more than 100,000 people. People went to the city center, and the joy was universal. It is understandable, such things do not happen often," said a city official.

Russia will face Croatia in the quarter-final match in Sochi on Sunday (AEST).