South Korea had recovered from a goal down to lead 2-1 and looked on the verge of securing their first World Cup win before Karla Villalobos ran onto a fine pass in the box and stroked home the equaliser from eight yards out.
The Montreal match was open, fast and skilful and a big improvement over the poor 1-0 win that Brazil had earlier scraped over Spain to qualify from the group with six points.
Costa Rica are now in second place with two points while South Korea and Spain have one apiece. Costa Rica play Brazil in their final game while South Korea play Spain.
Costa Rica took the lead in the 17th minute when Melissa Herrera latched onto a long free-kick into the box to lob the ball into the net.
The Koreans tied the match in the 21st minute when Ji So-yeon scored from the penalty spot after the Italian referee awarded the kick following an innocuous collision in the box.
Jeon Ga-eul then put South Korea ahead in the 25th minute, meeting a cross from the right with a lovely cushioned header.
(Editing by Peter Rutherford)
