The decisive penalty once again fell to Rakitic, though, and he confidently rolled the ball into the bottom-left corner to keep Croatia's dreams of a first World Cup final alive.
In the end, the team went down to an agonizing 4-3 penalty shootout defeat after the scores had finished level at 2-2 following extra-time.
Starting the penalty shootouts with a miss, Russian Federation could not save their World Cup dreams as Ivan Rakitic scored the deciding kick that saw Croatia through to the semifinal where they will face England. We'll have to focus more on defending from set pieces because we conceded today from a set-piece.
At 1-1, Fernandes missed his shot - only the second player to miss in any of the four shootouts at this year's World Cup. Croatia are in the semi-finals.
Then in 1990 in Italy they beat Cameroon in extra time to head into another semi-final, this time they faced Germany and lost on penalties, the beginning of their long hoodoo from 12 yards.
Russia's unlikely World Cup run has captured the imagination of the nation, with celebrations the length and breadth of the country after each of the team's wins in the tournament.
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Cheryshev was Russia's leading scorer at the World Cup with four goals.
"Luckily, I've been playing alongside him for the past 10 years and each game since he was named captain, he's been leading us with great power, strength and self-confidence".
Denis Cheryshev, who scored his fourth goal of the tournament when he gave Russian Federation the lead with a rasping left-footer from the edge of the box in the 31st minute, said the players left their all on the field.
"Putin phoned Cherchesov prior to the game on Saturday and wished him success", Peskov said.
"Talking about criticism, if they trusted us or not, we trusted ourselves".
Much of the build-up to the quarter-final match has centred on the iconic 1998 team as the present meets the past.