Denis Cheryshev put the hosts ahead with a stunning 20-yard strike, but they required a 115th-minute header from Mario Fernandes to take the game to spot-kicks after goals from Andrej Kramaric and Domagoj Vida.
Meanwhile, Croatia beat Nigeria (2-0), Argentina (3-0) and Iceland (2-1) to win Group D with 9 points.
More memes, more cheers, more tears will come next week, when France plays Belgium on Tuesday, and England takes on Croatia on Wednesday.
Croatia's Dejan Lovren and team mates celebrate winning the penalty shootout.
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Other judges that have been widely considered to be finalist include Brett Kavanaugh , Raymond Kethledge and Amy Coney Barrett . And Kavanaugh also worked on "The Starr Report", which outlined the grounds for President Bill Clinton's impeachment.
Croatia appeared to have the tie in the bag after Vida's extra-time goal until Fernandes rose to head in a free kick and send both teams to their second penalty shootout of the tournament.
Croatia goalkeeper Danijel Subasic, already hobbled with a leg injury, could do nothing but watch it hit the net. We've succeeded but I believe we can make further steps forward.
Cheryshev's troops were pressurising the Croats looking for the equaliser but the Vatreni managed to go into the break of extra time leading 2-1.
But all of Russian Federation held its collective breath when a shot from Ivan Perisic on the hour mark struck the inside of the post and the ball somehow rolled across the face of the goal to safety - the Croatian winger couldn't believe he hadn't scored. There was not a single national team in the World Cup that had the complete trust of their country.
Rakitic and Iniesta won three La Liga titles, four Copa del Rey trophies and a Champions League together between 2015 and 2018, and the Croatian said he was stunned that Fernando Hierro overlooked the World Cup victor as Spain went up against Russian Federation in the round of 16.