The 2018 runners-up came through their second straight shootout after beating Japan also on penalties in the last 16 and will now face either the Netherlands or Argentina who play each other later.
In an evening filled with tension and drama, Brazil superstar Neymar thought he had won the game when he rifled in an extra-time goal for the five-time world champions.
But instead of protecting their fragile lead they went in search of a second goal and were punished when substitute Bruno Petkovic drilled in an equaliser with their one and only shot on target three minutes from the end of extra time, breaking Brazilian hearts in the Education City Stadium.
The Croats, who needed two shootouts and an extra-time win to reach the final in 2018, then kept their composure from the penalty spot as Brazil's Marquinhos and Rodrygo failed to convert.
"This is just for the Croatian people," said coach Zlatko Dalic. "A great match from the first minute to the last. We eliminated the biggest favourites. This is not the end for us, let's keep going.
"This is a victory for all of us, everyone gave their best. Thanks also to those on the bench, who also live for this national team."
NOT INTIMIDATED
Croatia refused to be intimidated by their more illustrious opponents and in the first half successfully stifled most Brazil moves early.
Apart from a weak Vinicius Jr. shot, Brazil had little to offer in terms of attack with Neymar off the pace and shut out by a hard-working backline.
It was Croatia who looked sharper, more skilled in their passing game and with a precise game plan, and by the end of the first half they had the upper hand in terms of possession.
A Neymar free kick just before the break did not trouble Croatia keeper Dominik Livakovic as the Brazilians, whose last win over a European opponent in the knockout phase came in their 2002 final victory over Germany, struggled to find space.
They did, however, enjoy a stronger start after the break with Croatia defender Josko Gvardiol almost scoring an own goal.
Claims for a hand ball by defender Josip Juranovic were shot down following a VAR review before Neymar was sent through by Richarlison in the 55th minute only to have his close-range effort blocked by Livakovic.
The Brazilians, who have now lost four of their last five World Cup quarter-finals, all to European opposition, came close again in the 66th when Lucas Paqueta was denied by Livakovic.
KEEPER BUSY
The Croatia keeper was kept busy and again stopped Neymar in the 76th and by that time had more saves in the match (seven) than his Brazil counterpart, Alisson, had in the entire tournament (five).
Livakovic then parried another Paqueta shot five minutes later as the few hundred Brazil fans in the stands grew louder and more impatient and the game trickled over to extra time with Brazil coach Tite visibly nervous.
In stoppage time of the first period, Neymar launched an attack outside the box, played two consecutive one-twos to bamboozle the tired Croatian defence and then rounded the keeper to equal Brazil great Pele's record of 77 international goals.
But it was not enough and the Croats snatched a late Petkovic equaliser forcing penalties.
They then came out on top in the shootout with Livakovic saving Rodrygo's spot kick and Marquinos hitting the post, leaving Neymar and his team mates in tears and Croatia dreaming of their first world title.
