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 playoff first-leg victory, having led Iceland to second place in Group E.
Croatia, meanwhile, got off to a flying start in Group A - winning five of the opening six fixtures - but tailed off dramatically in the final four matches and the team is without a competitive victory since a 2-1 win over Wales in March.
That poor form led to the dismissal of head coach Igor Stimac, so former Croatia captain Niko Kovac will begin his interim tenure in charge of the national side under huge pressure.
Both sides finished their group campaigns on 17 points - a distant second behind Switzerland and Belgium respectively - and, aside from Denmark, which missed out on the playoffs, and France, which featured in a smaller group, Iceland and Croatia were the lowest point-scoring runners-up of the group stage.
While Iceland is aiming to qualify for its first tournament, Croatia has missed out just once since its first entry in 1998.
The history books will make unhappy reading for Iceland fans, with Croatia having won the two previous competitive encounters between the sides, scoring seven goals and conceding just one in reply.
Despite his side's lack of major tournament experience, Lagerback is hopeful Iceland - where the 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."
Iceland will look to Kolbeinn Sigthorsson to boost its chances of victory, the Ajax man has netted 13 goals in 19 games for his country.
Meanwhile, defender Birkir Mar Saevarsson is suspended for the home side for the first leg.
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.
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