Danijel Subasic saved another penalty and Ivan Rakitic converted the decisive one as Croatia ended the fairy-tale run of World Cup hosts Russian Federation with a 4-3 win on penalties on Saturday to set up a semi-final date with England.
The teams then went back and forth in regulation, and neither could find the victor, sending the game into extra time.
Working the ball quickly upfield near the sideline, Croatia got the ball into the box on the feet of Mario Mandzukic, who fed in a cross for Kramaric to head home from eight yards.
For Croatia, Mateo Kovacic had his penalty saved, but Marcelo Brozovic, Modric and Vida all netted theirs before Rakitic stroked in the victor.
The goal swung the momentum of the contest the way of Croatia and they should have completed the comeback but after Igor Akinfeev flapped at a cross, Perisic could only strike the loose ball against the inside of the post.
The crowd erupted, but Croatia were undeterred and equalised just eight minutes later.
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However, it was not to be for the resilient hosts, with goalkeeper Danijel Subasic saving Fedor Smolov's penalty and Fernandes firing wide before Rakitic kept his composure to put Croatia one match away from the final.
Domagoj Vida headed home what looked like being the victor in the 100th minute, but with five minutes remaining Mario Fernandes flicked home to send the game to penalties after a 2-2 thriller.
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.
The match started at a high tempo, with Russian Federation not giving the Croats space and time to play in the middle of the park. Assisted by Luka Modric with a cross following a corner. Assisted by Alan Dzagoev with a cross following a set piece situation.
And it remains to be seen how quickly Croatia - whose President Kolinda Grabar-Kitarovic was watching from the stands in her country's colours - can recover from this draining night, having also been taken to extra time and penalties by Denmark in the last round.
Fernandes' header sent the Fisht Olympic Stadium wild.