Lars Lagerback, whose career has seen him manage at three World Cups already, will now be looking to give himself every chance of reaching a fourth with a play-off first-leg victory, having led the European minnows to second place in UEFA Group E.
Croatia, meanwhile, got off to a flying start in Group A - winning five of their opening six fixtures - but tailed off dramatically in their final four matches and are without a competitive victory since a 2-1 win over Wales in March.
Despite his side's lack of major tournament experience, Lagerback is hopeful Iceland - whose high-profile players include Tottenham's Gylfi Sigurdsson and former Chelsea and Barcelona man Eidur Gudjohnsen - can upset the odds and make history.
"Of course it would be a huge disappointment if we didn't get to Brazil now that we are so close but, as far as I am concerned, we are in a win-win situation," he said.
"There weren't many outside Iceland and, to be fair, on Iceland who expected us to get this far, even though the expectations have grown the further we have got in qualifying.
"But I hope people are not thinking that (it would be a huge disappointment to miss out). I am certainly not thinking that way."
Croatia left-back Ivan Strinic is unavailable due to injury but the likes of Luka Modric, Mario Mandzukic and Niko Kranjcar will be available to Kovac.
