And they started well.
Easy wins over Jamaica and Japan in the group phase meant a meeting with Romania, winners of England's group, in the first knockout round.
A twice-taken penalty from Davor Suker settled the tightest of contests with the Romanians and set-up a quarter-final clash with an off-colour Germany side.
Germany, who were fielding players nearing the end of their careers, such as Jürgen Kohler, Lothar Matthäus, Thomas Hassler and Jürgen Klinsmann, were thumped 3-0.
Incredibly Croatia, in their first World Cup ever, were now within one match of the final itself.
Now hosts France stood in their way.
Suker put Miroslav Blazevic's side ahead, but a defensive error allowed right-back Lilian Thuram to equalise with his first ever goal for France.
And just minutes later Thuram scored again to put France into the final and end brave Croatia's dream.
Croatia beat the Netherlands in the third/fourth place play-off but the after effects of coming so close to the ultimate prize and missing out lasted for a long time.
They miserably failed to qualify for Euro 2000, meaning they will be doubly-determined to make up for lost time once the finals get under way in the Far East.