Ivan Rakitic scored the decisive spot-kick as Croatia beat hosts Russia 4-3 on penalties to book a World Cup semi-final date with England.
After extra time ended with the score level at 2-2, goalkeeper Danijel Subasic was Croatia's penalty hero, denying Fedor Smolov before Mario Fernandes fired wide.
Rakitic stepped up to score the winning kick and earn his country a place in the semi-finals for the first time since 1998.
In a dramatic match, Russia had taken the lead through Denis Cheryshev's exceptional finish, the Villarreal player starting the move before finishing from outside the area after Artem Dzyuba's pass.
Former Leicester City striker Andrej Kramaric equalised after Mario Mandzukic had been afforded too much space to cross before the both teams were forced to settle for extra time for the second successive game at the tournament.
Croatia thought they had won it when Domagoj Vida struck from a corner in the 100th minute only for Fernandes to force penalties with a dramatic headed equaliser.