An estimated 10,000 fans will support captain Luka Modric's side in Zagreb's main square, where the World Cup matches are watched on a giant screen.
Thousands of others were expected at fan zones in the capital and other cities.
Football fever has ratcheted up in the country of around four million people, boosted by a thumping 3-0 group-stage win against Argentina and a victory on penalties against Denmark to reach the quarter-finals.
Cars are decorated with red-and-white chequerboard flags and football jerseys are being sold in large numbers.
"Modric is bestselling, although (Danijel) Subasic is becoming increasingly popular," Ana Maric, 20, selling souvenirs in downtown Zagreb, told AFP.
Goalkeeper Subasic was the hero against Denmark, making three penalty saves.
If Croatia beat Russia they will meet either England or Sweden in the semi-finals.
Croatia's only previous appearance in the quarter-finals came in their first-ever World Cup as an independent nation, in France 20 years ago. Eventually they ended up third.
"22 'Fiery Ones', One Heart, One Soul, One Croatia!" trumpeted the Sportske Novosti paper, featuring photos of the players.
"Night for immortality! -- We trust! We go to semi-final!" said the headline.
Labelling it the "crucial match of this generation", it noted that "Russia is a superpower for Croatia in everything except in football".
"The 'Fiery Ones', the best ambassadors of Croatia in the world... will try to break a big 'Russian bear'."
For the influential Jutarnji List paper, the match is a chance for Croatia to match the success of the 1998 squad, which included Davor Suker and Zvonimir Boban.
Coach Zlatko Dalic said Saturday the "whole country is euphoric".
Croatia fans will be massively outnumbered in a crowd of more than 40,000 in Sochi, but Dalic's team are expected to have one notable backer -- President Kolinda Grabar-Kitarovic.