The Bosnian outfit head into the second leg of this tie having established a 6-2 aggregate lead ahead of their trip to Iceland.
Match preview
When Breidablik and Zrinjski were paired together in the third qualifying round of the Europa League, one thing became clear: One of these sides would be guaranteed group-stage football in Europe for the first time ever.
With the winner of this tie having the minimum of a Europa Conference League spot in their possession for September onwards, the stakes were high ahead of the opening leg in Bosnia-Herzegovina.
Neither side could claim to be overwhelming favourites based on their recent form, yet it was Zrinjski who made a mockery of that perception as they prevailed by a 6-2 scoreline.
They were five goals to the good at half time - helped by the 31st-minute dismissal of Viktor Karl Einarsson - and there would have been a tinge of disappointment with how they ended the opening contest.
Nevertheless, Krunoslav Rendulic and his side have put themselves on the brink of creating history and will expect to do so having had a week to prepare for the reverse fixture.
Although they have only won two of their five European fixtures this term, their two defeats have been by one-goal margins, highlighting the size of the task in front of Breidablik.
That particularly rings true when the Icelandic side are without a victory in six games in all competitions, conceding 17 times in their last 360 minutes of action.
While a 1-1 draw was recorded against KA at the weekend, it left Oskar Hrafn Thorvaldsson's team as many as 15 points adrift of first place in the top flight.
At a time when they will be dreaming of one of the best comebacks in European footballing history, regaining some form ahead of the likely demotion to the third tier of continental football is more realistic.
Breidablik Europa League form:
L
Breidablik form (all competitions):
Zrinjski Mostar Europa League form:
W
Zrinjski Mostar form (all competitions):
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Team News
With Einarsson suspended, Jason Dadi Svanthorsson may switch to the right flank, but Thorvaldsson then has a decision to make regarding who comes into the side.
Using Klaemint Olsen as a second forward is a possibility, while teenager Agust Orri Thorsteinsson may be handed a chance on the left.
Meanwhile, Zrinjski defender Hrvoje Barisic was substituted through injury less than half-an-hour into the first leg.
The defender was replaced by Matej Senic, and that will theoretically be the only change providing that Rendulic opts to name his strongest XI.
Breidablik possible starting lineup:
Einarsson; Yeoman, Margeirsson, Muminovic, Gunnlaugsson; Eyjolfsson, Sigurjonsson, Ludviksson; Svanborsson, Steindorsson, Thorsteinsson
Zrinjski Mostar possible starting lineup:
Maric; Corluka, Jakovljevic, Senic, Ticnovic; Ivancic, Kis, Canadija; Malekinusic, Bilbija, Cuze
We say: Breidablik 2-2 Zrinjski Mostar (Zrinjski Mostar to win 8-4 on aggregate)
Facing a four-goal deficit, Breidablik have little choice but to go on the offensive from the off in this game. However, that will only provide the visitors with extra space to put the tie out of their hosts' reach, and we expect Zrinjski to cruise over the line.