On both ends of the field, Sime Vrsaljko got the job done.
The Croatia defender set up the equaliser in the second half and then saved a likely goal by clearing a shot off the line in the first half of extra time.
Those two moments of excellence helped Croatia reach their first World Cup final following a 2-1 win over England on Wednesday.
Vrsaljko, who plays for Atletico Madrid, had struggled to be ready for the match after playing in two previous extra-time matches, but he found the strength to lift his tired, battered team to a comeback win.
The victory sets up a final against France on Sunday and improves Croatia's previous best showing at the World Cup, which ended in a 1998 semifinal loss to hosts France.
With Croatia trailing 1-0, Vrsaljko curled in the cross that Ivan Perisic volleyed into the net in the 68th minute.
In extra time, he leapt high to block John Stones' header, keeping Croatia in the game before Mario Mandzukic scored the winning goal about 10 minutes later.
The Croats entered the match after winning their previous two games on penalty kicks, but they showed no sign of fatigue in the second half against England.
With three straight extra-time matches, Croatia have played the equivalent to a full 90-minute match more than France has through six games in Russia. France also have an extra day of rest after beating Belgium 1-0 on Tuesday.
Besides scoring, Perisic also hit the post for the second straight game and set up Mandzukic's winner, heading a poor clearance toward the Juventus striker to score.
Australian Associated Press