Croatia, beaten finalists four years ago, scored with all four of their spot-kicks as Rodrygo – taking his team’s first kick – was denied by the brilliant Dominik Livakovic and Marquinhos’ crucial fourth effort struck the post.
After an engrossing 90 minutes, Tite’s men thought they had won it in extra time when Neymar scored a thumping effort to equal Brazil’s ‘official’ men’s goalscoting record.
But substitute Bruno Petkovic had other ideas, stroking in a 116th-minute equaliser with Croatia’s first shot on target in the match to take the game to the nerve-shredding shootout.
And it was the European side who emerged victorious once more, having done so by the same method against Japan in the last 16, to set up a semi-final meeting with the Netherlands or Argentina on Tuesday.
Brazil were supposed to dance through to the last four in their quest for another star on their shirt but their hopes were ended in the cruellest fashion.
Neymar, who scored his 77th international goal to equal Pele’s official mark, now shares a record recognised by Fifa but not the national team – as they also counted goals netted by their three-time World Cup winner in friendlies against club sides.
And the Paris St-Germain forward will not get the opportunity to surpass the legend at this tournament, as Brazil suffered woe against a European nation once again. Since beating Germany in the 2002 final, they have been knocked out of five successive World Cups by a team from Europe.
This was supposed to be Neymar’s moment, standing up for his side when they needed him most with a clinical finish to complete a slick team move, but he was left in tears after the shootout.
He should have won it for them in normal time but neither he nor Lucas Paqueta could find a way past the inspired Livakovic, who made a total of 11 saves, the most by a goalkeeper at this tournament.
Though most were routine, Livakovic had to be in the right place at the right time to make the stop and he certainly was with Brazil’s first penalty, diving the right way to push out Rodrygo’s strike.
Croatia are a well-organised and stubborn outfit, but they did not managed a shot on target until four minutes from the end of extra time, as Petkovic’s side-footer beat Alisson.
Zlatko Dalic’s men displayed their mental fortitude and powers of endurance once more to go through – as eight of their past nine knockout matches at major tournaments have now ticked into extra time.
Once this one went to penalties, Nikola Vlasic, Lovro Majer, the evergreen Luka Modric and Mislav Orsic were all successful with their efforts, while Neymar was not among the first four Brazilians penalty-takers, presumably left to take a decisive fifth which never came.
The second successive shootout success for Croatia sends them through to their third World Cup semi-final.