Danijel Subasic saved three penalties, and Croatia's World Cup hopes.
In the second straight shootout of the tournament, the Croats advanced to the quarterfinals with a 3-2 victory over Denmark on penalties following a 1-1 draw on Sunday.
Subasic tipped the first penalty from Denmark midfielder Christian Eriksen onto the post. He then dived to his right to save an attempt from substitute Lasse Schone. Finally, he used his feet to block Nicolai Jorgensen's attempt.
Subasic is only the second goalkeeper to save three penalties in a shootout at the World Cup. The only other man to do it was Portugal keeper Ricardo against England in 2006.
Croatia will next face host Russia in the quarterfinals on Saturday in Sochi. Russia also advanced on penalties, beating Spain 4-3 following another 1-1 draw.
Croatia had a chance to take the lead late in the game at Nizhny Novgorod Stadium, but Luka Modric's penalty was saved by Kasper Schmeichel. The Denmark goalkeeper, who also saved a pair of penalties in the shootout, dived to his left to smother Modric's attempt in the 116th minute.
Subasic's three saves and Schmeichel's two made it the most combined saves in a World Cup shootout.
Modric, however, made his penalty in the shootout and Ivan Rakitic scored the decider with a shot to the left side of the net as Schmeichel dived the wrong way.
Croatia entered the match after impressing in the group stage, including a 3-0 dismantling of two-time champion Argentina at the same stadium. But Denmark, unbeaten in 18 games coming into the game, provided tough opposition.
The Danes took the lead in the first minute when defender Mathias Jorgensen scrambled in a shot that went in off Subasic's left hand and then the left post. It was Denmark's fastest ever World Cup goal.
Croatia equalized in the fourth minute with another untidy goal. Henrik Dalsgaard's clearance hit a teammate and fell for Croatia forward Mario Mandzukic to hook the ball in.
The teams stayed even for the next 116 minutes, including the 30 minutes of extra time.