Croatia are into the semi-finals of the World Cup for the second time in their history thanks to a penalty-shootout win over Russia at the Fisht Olympic Stadium, following a 2-2 draw after extra time.
Two decades on from their only other run to the last four, the Vatreni can plan for a showdown with England in Moscow next Wednesday after holding their nerve in the sudden-death situation for the second match running.
The two sides made a change apiece from their last-16 ties - Cheryshev replacing the injured Yuri Zhirkov for Russia, who reverted to a back four, and Kramaric taking over from Marcelo Brozovic for Croatia.
A quiet opening quarter to the contest transpired with little incident, although it was Croatia who were looking the more lively.
From pretty much nowhere, though, Cheryshev blasted his side in front from only their third shot on target in two-and-a-half games.
Croatia, beaten in just three of their last 22 competitive outings prior to this game, responded well and were back on level terms eight minutes later.
Kramaric came close to doubling his tally with an acrobatic attempt early in the second half that was aimed too close to Akinfeev.
Russia were inviting more and more pressure on themselves as they focused on counter-attacking opportunities, which was proving to be a dangerous strategy.
After falling apart at the back, Russia so nearly fell behind as Ivan Perisic picked up a loose ball and guided it towards the bottom corner, with the post coming to Sbornaya's rescue.
Dzyuba made clean contact with a cross at the other end from a rare Russian delivery into the box, while substitute Aleksandr Yerokhin failed to find the target from a similar position 10 minutes later.
Neither side did enough to deserve a goal in a disappointing second half, however, meaning that extra time would be required in Sochi.
What looked like being the decisive moment then arrived - Vida rising highest near the penalty spot to send a poorly-conceded corner into the bottom right of the net.
Russia chucked bodies forward in a desperate attempt to keep their World Cup adventure alive, and it paid off as Fernandes flashed a header into the bottom left from Alan Dzagoev's perfect free-kick delivery.
Roman Zobnin had a low shot saved from the final meaningful act of extra time, ensuring that both teams would again be forced to partake in a penalty shootout.
Smolov and Fernandes both missed for Russia, as did Mateo Kovacic for Croatia, and it was then left to Rakitic to convert the winning spot kick.
RUSSIA (4-4-1-1): Akinfeev; Fernandes, Kutepov, Ignashevich, Kurdjasov; Samedov (Erokhin 54'), Kuzyayev, Golovin (Dzagoev 102'), Zobnin; Cheryshev (Smolov 67'); Dzyuba (Gazinskiy 79')
CROATIA (4-2-3-1): Subasic; Vrsaljko (Corluka 97'), Vida, Lovren, Strinic (Pivaric 74'); Rakitic, Modric; Rebic, Kramaric (Kovacic 86'), Perisic (Brozovic 63'); Mandzukic