Under the guidence of their Swedish coach Lars Largerback the island nation, with a population just over 300,000, is on the cusp of reaching a major tournament for the first time in its history.
Largerback steered Sweden to five successive major tournaments between 2000 and 2009, but admits should he take Iceland to Brazil next summer it would be a more significant achievement.
"We have been underdogs the whole time," he told a press conference on Thursday.
"Many asked me when I took the job: 'Why take Iceland? What chance do you have?',"
"If we succeed now, when nobody has given us a chance - you heard the play-off draw, everyone wanted us - if we do it, it would mean a little more than qualifying with Sweden.
"From being a small country and not believing it in the beginning, it's bigger in that way."
Iceland had won just two of its previous 16 qualifiers before Largerback took over and were the lowest-ranked nation in Group E when the draw was made.
They turned that record on its head winning five of their group games, including successes over Norway and Slovenia, and are unbeaten in their past four including a 4-4 draw at group winners Switzerland.
Largerback puts the turnaround, which has seen them rise to 46th in the world rankings, down to changes made in Icelandic football in the previous last decade.
A group of young players has emerged - Kolbeinn Sigthorsson (Ajax) and Gylfi Sigurdsson (Tottenham) both scored four times in qualifying - to provide depth behind more recognisable names such as former Barcelona and Chelsea veteran Eidur Gudjohnsen.
"Six or seven years ago they built seven full-size indoor pitches. That means that they can train and play football year-round," he said.
"Then there's been a generation of young players who went to the 2011 European Under-21 finals in Denmark. They're the framework of the team now. A lot of them have gone to good clubs and they're all playing."
Despite Iceland's vast improvement, Croatia are the heavy favourites to progress to a World cup finals for the first time since their group-stage exit in 2006.
They will head into the play-off with a new coach, however, after Igor Stimac stood down following a 2-0 defeat in their final World Cup qualifer against Scotland last month.
Niko Kovac has taken over and has targetted at least an away goal against a team he concedes is better than some have given them credit for.
"Our first priority in Iceland will be to score an all-important away goal and we also want to look like a decent team," he said.
Kovac also confirmed first-choice left-back Ivan Strinic was out with an abdominal injury and wil be reaced by Danijel Pranjic.
Striker Ivica Olic is also set to miss out in Reykjavik, but Kovas expects he will be back for the second leg in Zagreb next Tuesday.
"The situation is complicated with Strinic and we won't know the extent of his injury before a scan but Olic should be fit for the return leg because it looks like a strain rather than a torn muscle," he said.