Croatia will face England on Wednesday, July 11th.
Russian Federation took the lead in the 31st minute when Croatia failed to close to Cheryshev and the Villarreal midfielder fired a rocket from 20 yards out past the stranded Subasic.
When Russia finally bowed out, shortly before midnight local time with defeat on penalties against Croatia in their quarter-final, they were departing the festival a good five hours of playing time later than many had forecast.
The teams then traded two scores each before Ivan Rakitic calmly converted the winning penalty.
Yuri Gazinskiy became Russia's third substitutes, coming in for Dzyuba, but Croatia almost ran into trouble after making two more subs, Josip Pivaric and Mateo Kovacic on for Ivan Strinic and Kramaric. It became 1-1 when Alan Dzagoev scored and Mateo Kovacic flopped.
The two nations had met on three previous occasions with the Croats triumphing 3-1 in a friendly in 2015, after two goalless draws in qualification for the 2008 UEFA European Championship. Luka Modric, who was yet again the best player on the pitch for Croatia, sent shivers down the spines of his compatriots when his penalty hit the bar, but it had sneaked in past Akinfeev. Croatia, in turn, scored Russian Federation on penalties. That strike was canceled out eight minutes later by a Andrej Kramaric header. Subasic soldiered on and he had to as Mario Mandzukic and Sime Vrsaljko both started limping. The expense of a penalty kick 1:0.
After a tense first half hour, Denis Cheryshev gave Russian Federation the lead with an unstoppable long-range effort.
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The first clear chance for the hosts fell to Artem Dzyuba on the volley, who cannoned a shot off Lovren's backside from ten yards out.
Russian Federation endured the penalty pain for a change, after having inflicted the same on Spain in the Round of 16. Igor Akinfeev was more than once called into action in the opening moments and each time displayed his class that was so apparent versus Spain to keep Ante Rebic's effort out.
After hardly seeing the ball in the round of sixteen, Stanislav Cherchesov's side will be looking to play a slightly more expansive game at the Fischt stadium and will be cheered on by an expectant home crowd.
Croatia did not get through the group stage in the next three attempts but now they are back in the semis, and determined to take the next step.
- Only one of the last six World Cup matches to go to extra-time has not gone to penalties - the 2014 final between Germany and Argentina.
Croatia would not miss again, with FC Barcelona star Ivan Rakitic scoring the victor into the bottom left of the goal. After it finished 1-1 in normal time, both teams scored one each in extra time. Modic will have to show leadership in Sochi if Croatia is to make it to the semi-finals for the second time in their history.
Croatia booked a semi-final spot against England but their performance yet again mirrored their shirts - chequered. Watch the Live & Exclusive stream of the game on MAX HD3 & beIN SPORTS CONNECT.