The Norwegians, who were only fourth at the last European championships, will face defending champions France in Sunday's final.
France will be going for a sixth world crown and will be buoyed by knowing that they beat Norway, who only qualified for the championships after being granted a wildcard, 31-28 in the preliminary round.
But Norway, who failed to make the Olympics in Rio, know that they have the measure of France having defeated them 29-24 at the European championships in Poland last year.
Goalkeeper Torbjorn Bergerud was named man of the match in Friday's semi-final after the 22-year-old pulled off a fine save from a penalty taken by Zlatko Horvat in the last minute of normal time.
That kept the score at 22-22, sending the tie into two five-minute periods of extra-time.
Croatia, world champions in 2003, led 24-22 in the extra period but the faster style of Norway eventually paid dividends.
France defeated Slovenia 31-25 on Thursday to reach the final and get to within touching distance of a sixth major international title.
France, world champions in 1995, 2001, 2009, 2011 and 2015, will start as favourites on Sunday having seen Olympic champions Denmark and European champions Germany knocked out in the last 16.