It also meant that Croatia became the first side to win two penalty shootouts in a single World Cup campaign since Argentina in 1990. The host nation lost 4-3 the penalty shootout, which followed 2-2 draw in the regular and 30-minute overtime period.
The 1998 team made a quarter-final statement, sending German football into a spin with a 3-0 win and they were 1-0 up against hosts France in the semi-final before losing 2-1.
They were both, at various times, supposed to be in charge of making the host nation's team fit for goal at the landmark event for the country.
Russia's Denis Cheryshev scores his side's opening goal during the quarterfinal match between Russia and Croatia at the 2018 soccer World Cup in the Fisht Stadium, in Sochi, Russia, Saturday, July 7, 2018.
Fernandes, who was born in Brazil but rejected a chance to play for that country's national team in 2011, sent his penalty kick wide of the net in the shootout, giving Croatia the advantage.
Ten minutes into extra time, Vida put Croatia ahead and seemingly on course for victory but, with Russian Federation looking dead and buried, Fernandes appeared from nowhere to haul the host level in the dying minutes of extra time.
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While the result was bad news for Cilic, Federer must have been watching with a wry smile as he avoided the Queen's champion. Keys also came up short with a comeback attempt after fighting back from a set and two breaks down, losing 7-5, 5-7, 6-4.
But only eight minutes later an Andrej Kramaric header amid slack marking brought Croatia level, and after the break Ivan Perisic saw a low shot crash against the post and out across the face of goal as Zlatko Dalic's side began to control the game.
With the scores locked at 1-1 after full time, the match went into extra time where Domagoj Vida's header gave Croatia the lead in the 110th minute but once again Russian Federation would rise to the ocassion through Brazillian-born Mario Fernandes in the 115.
The crowd erupted, but Croatia were undeterred and equalised just eight minutes later.
Going behind to Russian Federation after 30 minutes having quietly enjoyed the better chances of the match, Croatia showed England where they can be got at as gaps showed in front of their defence.
The game went to penalty kicks - where Russia's penalty takers made one too many mistakes from the spot.
Most certainly a candidate for the best goal of this World Cup.
Cheryshev, who scored three times in the group-stage wins over Saudi Arabia and Egypt, was back in the line-up here after beginning on the bench against Spain last weekend. That all changed in spectacular style as Cheryshev won the ball in midfield, exchanged a one-two pass with striker Ayrtom Dyzuba before swerving a rocket that dipped into the top corner of the Croatia goal to open the scoring. But he kept going and pulled off a series of saves in extra-time before reading Fyodor Smolov's intention of a cheeky Panenka penalty in the shoot-out. And his header late in extra-time carried Russia's fairytale further than seemed credible, an equaliser for 2-2, and into a second successive penalty shoot-out.