Luka Modric admitted Croatia were shattered after they ended Russia's World Cup hopes in another penalty shootout on Saturday to advance to a semi-final against England.

Ivan Rakitic scored the winning spot-kick in Sochi at the end of a draining and rollercoaster last-eight clash that finished 2-2 after extra time.

Brazilian-born Mario Fernandes kept Russia's dream alive when he headed home in the 115th minute to level the scores and force penalties, but he and Fedor Smolov both failed to convert their spot-kicks and Croatia won the shootout 4-3.

Denis Cheryshev had put Russia in front in the first half but Andrej Kramaric and Domagoj Vida scored for Croatia before the late leveller from Fernandes.

Croatia advance to their first World Cup semi-final since 1998, against England in Moscow on Wednesday.

But it remains to be seen how quickly the team -- with President Kolinda Grabar-Kitarovic watching from the stands -- can recover from their efforts, having also been taken to extra-time and penalties by Denmark in the last round.

"At certain moments we lacked power but that's twice in six days that we have played 120 minutes," said skipper Modric.

"Of course this will leave a mark on you. You have to pay a price for such exertions."

Croatia will now look to go one step further than the great side of 20 years ago, who lost to France in the last four.

"It makes us extremely proud and happy to have reached the semi-finals again," Modric added.

"We took a difficult route. We were unlucky at previous tournaments but now we are collecting those debts this year, and hopefully we will go a step further than in 1998."

While Croatia coach Zlatko Dalic shed tears of joy at the end, for Russia there was heartbreak. But they can be proud of their efforts, with a run to the last eight exceeding expectations for a side written off as no-hopers before the tournament.

"We just wanted to prove ourselves," said coach Stanislav Cherchesov. "The entire country is in love with us, they know what the Russian national team is worth."

The Russians, riding a wave of euphoria after unexpectedly knocking out Spain in the previous round, came to the Black Sea beach resort determined to carry on to a first World Cup semi-final since the break-up of the Soviet Union.

But Croatia were the favourites. They dominated the match, even if Russia contributed to another fantastic occasion in what has been an outstanding World Cup.

The hosts went ahead thanks to a bolt from the blue just after the half-hour mark.

Cheryshev, back in the starting line-up, cut in from the left, exchanged passes with Artem Dzyuba and skipped away from a Modric challenge before firing home a superb shot from 25 yards.

Croatia were stunned. But the Russian lead lasted only eight minutes before they drew level, Mario Mandzukic cutting the ball back for Kramaric to head home.

Ivan Perisic hit the post for Croatia in a second half they controlled but they had to wait until the 101st minute to go in front, defender Vida heading in a corner before removing his shirt as he ran away in celebration.

However, Russia dug deep to make it 2-2, substitute Alan Dzagoev curling in a free-kick for Fernandes to head home in the 115th minute.

"For Croatia being in the semis is a great success," said Dalic. "Of course there is some power left for the English. We do not want to stop."