Russia coach Stanislav Cherchesov said, "We trusted ourselves. We could only prove our worth by working hard. I believe that people did not only start trusting us but they are in love with us."
In the regular time, Russia broke the ice first in the 31st minute when Villarreal midfielder Denis Cheryshev completed a neat one-two with forward Artem Dzyuba at the edge of the box, opened up space with a touch and swerved a stunning strike into the top left corner.
Modric, the Man of the match, said, "Another drama for us. We didn't play well in the first half, we didn't control the game as we wanted."
Smolov came off the bench to replace Cheryshev in the 67th minute to keep pressure in the front with Dzyuba, and the Russian formation was shifted to 4-4-2.
Instead of focusing on defense, Russia launched waves of attacks at the beginning. The first attack by Russia came quickly when Dzyuba received the ball from playmaker Aleksandr Golovin and found Cheryshev in the area.
Croatia coach Zlatko Dalic also fielded 4-2-3-1, trying to dominate the midfield with Modric's ability.
After a 2-2 tie after the extra time, Croatia beat Russia 4-3 in the penalty shootout, entering the World Cup last four for the first time in 20 years and breaking the jinx that they had no win over World Cup hosts after they lost to France in the semifinal in 1998 and Brazil in the opener in 2014.
Croatia coach Zlatko Dalic said after the game, "The Russia team fought well. This was not a beautiful game, it was a fight, a battle for the semifinal. We were lucky."
A stunning shot emerged in the 62nd minute when Croatian midfielder Ivan Perisic's effort from right to left hit the base of the post.
It was Cheryshev's fourth goal in his five matches of this World Cup. Only Harry Kane (6) has more in the tournament.
After Russia's blistering start, Modric-led Croatia gradually controlled the ball and the first half saw 65 percent ball possession for Croatia.
Russia coach Stanislav Cherchesov went back to a 4-2-3-1 formation with Fedor Kudryashov replacing the injured Yuri Zhirkov as a left-back. It could be either defensive or attacking, depending on the pressure applied by Croatia.
Eight minutes later, Croatian midfielder Andrej Kramaric headed in the equalizer on forward Mario Mandzukic's clinical cross from the left side of the Russian box.
After a 1-1 draw after the regular time, Vida headed in a dramatic corner in the 101st minute but he was booked a yellow card for taking off his jersey for celebration.
Croatia, who beat Denmark on penalties in the round of 16, are only the second team in World Cup history - after Argentina in 1990 - to win two penalty shootouts in the same edition of the tournament.
Croatia will next take on England, who tamed Sweden 2-0 in the third quarterfinal match hours before.
Russian forward Fedor Smolov, who came into the field as a substitute in the second half, came out first to the spot kick but saw his shot saved by the keeper. Defender Mario Fernandes, who equalized for Russia in the 115th minute with a close-range header, also missed the target.
Fourteen minutes later, Dzagoev curled in a brilliant free-kick from the right edge of the area and the unmarked Fernandes deftly headed the ball into the bottom corner to drag his team back from the cliff edge.
SOCHI, Russia, July 7 (Xinhua) -- Croatia triumphed on penalties, edging out hosts Russia in a breathtaking shootout here on Saturday in the World Cup quarterfinal duel, and will meet England in the semifinals in Moscow on July 11.
Roman Zobnin (R) of Russia vies with Luka Modric of Croatia during the 2018 FIFA World Cup quarter-final match between Russia and Croatia in Sochi, Russia, July 7, 2018. (Xinhua/Xu Zijian)
In the penalty shootout, Croatian substitute midfielder Marcelo Brozovic, playmaker and captain Luka Modric, defender Domagoj Vida and midfielder Ivan Rakitic all scored despite Mateo Kovacic's failure.
Kramaric became the seventh different player to score for Croatia at this World Cup - only Belgium have more names on the scoresheet (9).淮南新锦江大酒店招聘