Denis Cheryshev fired the hosts into a 31st minute lead with a spectacular strike but Andrej Kramaric headed home to make it 1-1 six minutes before the half-time break.
"One of the most important tasks for our team is to contain Modric, because he is a leading player in the Croatian team".
Real Madrid star Luka Modric, earlier goalscorer Vida and Barcelona midfielder Ivan Rakitic all converted their penalty kicks, handing the Croatians a 4-3 win in the penalty shootout.
Ivan Rakitic converted the decisive spot-kick after Mario Fernandes, who had netted an equaliser for Russian Federation with five minutes of extra-time remaining, hit his effort from 12 yards wide.
FIFA has fined the Croatian soccer federation over $70,000 for violating media and marketing rules at the 2018 World Cup in Russia.
But the fans also celebrated how far their team - the lowest-ranking side to qualify for this year's World Cup - had come, with crowds dancing and chanting "Russia" in the streets. The English team defeated Sweden 2-0.
Fernandes scored off Alan Dzagoev's free kick in the 115th minute, making the home crowd go insane and restoring faith at the time, when it appeared a semifinal berth was slipping away.
They have quickly been embraced as national heroes, with the mayor of Moscow responding by making additional public viewing space available in the city before the match in Sochi's Fisht Stadium.