Croatia overcame World Cup hosts Russia 4-3 on penalties following a 2-2 draw after extra-time to set up a semi-final showdown with England.
Ivan Rakitic struck the crucial spot-kick after Fedor Smolov and Mario Fernandes failed from the spot for Russia to settle a gritty quarter-final in Sochi on Saturday evening.
Denis Cheryshev's stunner (31) had earned Russia a first-half lead in front of a boisterous home crowd, but that was cancelled out eight minutes later when Andrej Kramaric headed in.
Domagoj Vida (100) headed Croatia in front in extra-time only for Fernandes to equalise five minutes from the end to take the game to penalties, but Stanislav Chercheshov's players were unable to replicate their shootout success over Spain and exit their own tournament at the quarter-final stage.
Russia: Akinfeev (6), Fernandes (7), Kutepov (6), Ignashevich (6), Kudryashov (6), Cheryshev (7), Kuzyaev (6), Zobnin (6), Golovin (7), Samedov (7), Dzyuba (7)
Subs: Yerokhin (7), Smolov (5), Gazinsky (6), Dzagoev (7)
Croatia: Subasic (7), Vrsaljko (7), Strinic (6), Lovren (7), Vida (7), Perisic (6), Rakitic (7), Kramaric (7), Modric (6), Rebic (6), Mandzukic (6)
Subs: Brozovic (6), Pivaric (6), Kovacic (6), Corluka (6)
Man of the match: Ivan Rakitic
Cheryshev had earlier sent the host nation into raptures with a stunning opening goal on 31 minutes, which will be remembered as one of the best of the 2018 World Cup.
The midfielder started the move himself in the centre circle, playing a one-two with striker Artem Dzyuba before taking a touch and unleashing a curling left-footed shot from the edge of the area which sailed into the top corner.
But the lead barely lasted eight minutes as Russia were undone by some sloppy defending. Mario Mandzukic found time and space on the left to drift into the penalty area and tee up an unmarked Kramaric to power home a header from the edge of the six-yard box.
There were precious few chances in a cagey second half, but Ivan Perisic should have won the game after an hour when he struck the inside of the post from eight yards after Sergei Ignashevich and Fyodor Kudryashov failed to deal with Mandzukic's cross
Russia made one change to the team that started the last-16 win over Spain, as Denis Cheryshev came in for Yuri Zhirkov. Croatia also made one change from the side that overcame Denmark in the previous round; Andrej Kramaric replaced Marcelo Brozovic.
However, Croatia's second goal arrived from an unlikely source 10 minutes into the extra-time period when Vida rose highest to head Luka Modric's corner down and past Igor Akinfeev.
But with five minutes left on the clock, Russia responded with a dramatic equaliser as Fernandes rose to head in Alan Dzagoev's free-kick and take the game to a penalty shootout.
Danijel Subasic saved Russia's first kick - a chipped effort from Smolov - but Mateo Kovacic saw Croatia's second effort saved after Roman Zobnin and Dzagoev both converted.
Russia's Fernandes put the next kick wide and there was to be no respite this time as Luka Modric, Vida and then Rakitic all scored to earn Croatia a second straight shootout win at this tournament and end the fairytale run of the unfancied hosts.
- Croatia are the second team to win two penalty shootouts at a single World Cup tournament - the other was Argentina in 1990.
- Russia are the first host country to be eliminated at the quarter-final stage of a World Cup since Mexico in 1986.
- Croatia have qualified for just their second World Cup semi-final, also reaching that stage in 1998.
- 14 of the 20 goals conceded by Russia at the World Cup have been scored via set pieces, including six of the seven they conceded at the 2018 World Cup.
- Croatia have now had eight different scorers at the 2018 World Cup - only Belgium (9) have had more.
- Both of Croatia's goals in this game were via headers - only one of their previous 29 World Cup goals was a header.
- There were three headed goals in this match - the most in a World Cup match since Germany 8-0 Saudi Arabia in 2002 (5 headers)
Man of the Match - Ivan Rakitic
This was a game full of drama, but lacking in quality. With Russia content to sit deep for long periods and Croatia's main outlet the overlapping runs of their right-back Sime Vrsaljko, they turned - as they so often do - to the creativity of their midfield duo. Luka Modric created the second Croatia goal, but was outshone by his partner Rakitic who produced an endless supply of raking passes and stepped up to nervelessly score the final kick of the shootout. Don't be surprised to hear plenty about him in the run-up to Wednesday night's semi-final.
Croatia will now face England at the Luzhniki Stadium in Moscow at 7pm on Wednesday evening for the chance to play either Belgium or France in the World Cup final the following Sunday.