FIFA World Cup Play-Off: Croatia v Iceland
Lars Lagerback's men held on for a 0-0 draw in the first leg in Reykjavik on Friday, despite seeing defender Olafur Skulason sent off early in the second half.
Iceland last came close to reaching a major competition during qualification for the 2004 UEFA European Championship, when they narrowly missed out on the play-offs after finishing a point behind Scotland in their qualifying group.
But Lagerback's side have the opportunity to etch their name into the history books on Tuesday, although they will need to record a first win over Croatia in order to do so.
Tottenham midfielder Gylfi Sigurdsson and Ajax striker Kolbeinn Sigthorsson are likely to be key to Iceland's fortunes, with both players having found the net on four occasions in qualifying.
Heerenveen striker Alfred Finnbogason could also have an impact if he can replicate the form that has seen him score 14 goals in the Eredivisie this season.
Iceland's clean sheet was only their third of qualification, and they will need to be at their best defensively if they are to keep a talented Croatia outfit at bay.
The hosts head into Niko Kovac's second game in charge on the back of a tumultuous group stage campaign, which saw Igor Stimac sacked following a 2-0 defeat to Scotland last month.
Kovac will require the likes of Real Madrid midfielder Luka Modric and Bayern Munich striker Mario Mandzukic to be on top form if they are to progress with victory in Zagreb.
Mandzukic has already scored eight times for Bayern in 2013-14, but his form in qualifying has not been as impressive, with the 27-year-old netting just three goals in 11 appearances.
Croatia have struggled for goals throughout qualification, finding the net only 12 times.
But, despite their poor form in front of goal and the disappointing result in Reykjavik, captain Darijo Srna has urged his team-mates to stay positive.
"Our fatigue is more of a mental nature than a physical one," he said.
"But we have to stay positive and win the game."