The two teams could not be separated at the end of 90 minutes, but Neymar struck for Tite’s side in stoppage time at the end of the first half of extra-time to send the South American nation ahead.
In finding the back of the net, the 30-year-old netted his 77th goal for the national side, which drew him level with Pele at the top of the goal scoring charts.
However, Croatia were level in the 117th minute through Bruno Petkovic, and the 2010 finalists went on to win the penalty shootout 4-2.
Croatia will now take on either Argentina or Netherlands in the semi-finals of the competition Tuesday.
The first shot of the match came in the fifth minute through Vinicius Junior, but the Real Madrid attacker’s effort was always comfortable for Croatia goalkeeper Dominik Livakovic.
Croatia had a chance of their own in the 13th minute when Mario Pasalic broke down the right before delivering a brilliant low cross towards Ivan Perisic, but the midfielder could not make contact at the far post.
Vinicius was the Brazilian player causing the majority of the problems to Croatia, and the attacker had a goal-bound strike blocked in the 21st minute after combining with Neymar inside the box.
Casemiro had one deflected wide of the Croatian post in the 23rd minute, before Perisic fired over the crossbar on the 30-minute mark, with both sides having their moments in the final third of the field.
Livakovic kept out a deflected Neymar free kick in the 42nd minute, but neither side made the breakthrough in the opening half of action, with Croatia certainly the happier of the two teams at the interval.
Brazil came close to making the breakthrough in the 47th minute when Raphinha’s low cross caused issues inside the Croatian box, but Josko Gvardiol just about did enough, before Livakovic kept out a close-range Vinicius effort after panic inside the penalty box.
There was a VAR check for a possible penalty on Josip Juranovic shortly after, but it was decided that the play should continue without any punishment for Croatia.
Livakovic was again called into action in the 54th minute to keep out a low strike from Neymar, before Lucas Paqueta was denied 25 minutes from time after the ball had broken kindly for the West Ham United midfielder.
The Croatian goalkeeper denied Neymar once more 15 minutes from time before keeping out a powerful drive from Paqueta with 10 minutes of normal time to play.
Eder Militao then had one deflected wide of the post, as Brazil continued to push for the winner, but Croatia held firm, with the match heading for an additional 30 minutes.
Brazil were the team on the front foot, but Croatia had a huge chance to take the lead in the 13th minute of extra-time when Marcelo Brozovic found room outside the penalty box, only to fire high of the target.
Tite’s side finally took the lead in the final stages of the first half of extra-time, with Neymar finding the back of the net at the end of a brilliant team move, with the Paris Saint-Germain attacker rounding the goalkeeper before finishing from a narrowing angle.
Croatia managed to level in the final moments, though, with Petkovic picking out the bottom corner from the edge of the box, albeit with the help of a deflection from Marquinhos.
Casemiro had a chance to win it late on, but his effort was saved, as the match headed for penalties.
Nikola Vlasic stepped up first for Croatia, converting down the middle for 1-0, before Rodrygo saw his spot kick kept out by Livakovic.
Lovro Majer then made it 2-0 to Croatia, but Casemiro answered back for Brazil with a brilliant effort.
Luka Modric was next, picking out the bottom corner for 3-1 to the 2018 finalists, before Pedro scored for Brazil to keep Croatia honest at a key stage of the shootout.
Mislav Orsic then found the bottom corner, before Marquinhos hit the post, with Croatia shocking the tournament favourites to advance to the final four.
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