Matej Senic scored the winner with only a minute of normal time remaining at Urartu Stadium in Armenia last week, making his side overwhelming favourites to progress to the next stage.
Match preview
Indeed, the record eight-time Bosnia & Herzegovina domestic champions are on the verge of reaching the second round of Champions League qualifying for the fifth time in their history, having exited at that stage on each of the last four occasions that they have made it there.
No team from Bosnia has ever qualified for the group stage of the Champions League, or Europa League for that matter, so head coach Krunoslav Rendulic will be determined to make history for both his club and the wider nation as a whole.
Rendulic led Zrinjski Mostar to one of their most emphatic ever title triumphs in the last campaign, with his side ending up 20 points clear of their nearest competitors in the shape of Borac Banja Luka.
Competing on a continental scale clearly provides them with a much greater challenge, but he will be demanding maximum effort and minimum complacency from his team when they look to protect their lead at Stadion pod Bijelim Brijegom on Tuesday.
Urartu, meanwhile, are competing in the Champions League preliminary rounds for only the second time after lifting their second Armenian Premier League last season.
Aryutsner were eliminated by Andorran side Santa Coloma at the first hurdle in the 2014-15 campaign, and they appear set to suffer a similar fate after Senic's last winner on their home turf last week.
In fact, Urartu have only prevailed from one of 16 two-legged ties which they have competed in across the Champions League, Europa League and Europa Conference League since the turn of the century, which was when they overcame Locomotive Tbilisi 4-3 on aggregate in 2005.
Interestingly, they also lost their home leg in that tie, with their 2-0 win in Georgia enough to carry them through to the next round. Their Russian head coach Dmitry Gunko will be hoping for a repeat of history in Bosnia on Tuesday.
Zrinjski Mostar Champions League form:
W
Zrinjski Mostar form (all competitions):
W
W
D
W
L
W
Urartu Champions League form:
L
Team News
Zrinjski Mostar are likely to remain without Marin Magdic and Ivan Jukic due to injury, with Rendulic unlikely to make any changes to his winning team from last week's first leg.
That could mean Mario Cuze is reduced to making an impact from the bench once again, having turned his loan move from last season into a permanent transfer earlier this summer.
Urartu, meanwhile, will travel without Sergey Mkrtchyan, Temur Dzhikiya and former Arsenal forward Yaya Sanogo due to long-term injuries.
Perisa Pesukic could make his first start for the visitors following his switch from FK Nozi Pazar last week, with Nana Antwi potentially making way for his new team-mate at right-back.
Zrinjski Mostar possible starting lineup:
Maric; Corluka, Senic, Barisic, Marin; Stanic, Canadjija; Ticinovic, Ivancic, Malekinusic; Bilbija
Urartu possible starting lineup:
Melikhov; Pesukic, Tsymbalyuk, Piloyan, Margaryan; Junior, Salou, Iwu; Grigoryan, Maksimenko, Sabua
We say: Zrinjski Mostar 1-0 Urartu
There was very little to split these two sides in Armenia last week prior to Senic's dramatic late winner, which has put the tie firmly in his side's own hands.
The visitors will have to show more offensive bravery than they managed in the first leg, but we can envisage the hosts doubling their lead in the tie at some stage, before successfully holding onto it.