One-nil winners in Bosnia, the Slovakian champions will play host at Stadion Tehelne Pole, where they were surprisingly held to a draw by Luxembourg's Swift Hesperange in the first round.
Match preview
With a third-round tie against either Sheriff Tiraspol or Maccabi Haifa at stake, Slovan Bratislava put themselves in good shape to progress by winning in Mostar last Tuesday, when Sharani Zuberu's second-half strike decided the game in their favour.
Despite having far fewer chances and much less of the ball, Slovan still prevailed at Stadion Bijeli Brijeg and will now benefit from the backing of their fans in this week's return leg.
Earlier this year, they lifted the Slovak Super Liga title for a fifth successive season, and the side overseen by former national team boss Vladimir Weiss are now aiming to reach the Champions League group stage for the first time in their history.
The Sky Blues' closest attempt to date saw them reach the playoffs nine years ago, but two more rounds must yet be navigated this summer even if they overcome Zrinjski.
Having regularly competed in the Europa League and Conference League in recent times - reaching the knockout rounds of the latter earlier this year - Slovan started their latest campaign quite sluggishly, only edging past little Swift Hesperange in the first round of qualifying after stumbling to a 1-1 draw on home turf.
The Bratislava club have since been held goalless by Kosice in their first fixture of the new Super Liga season; beginning the defence of their crown with an underwhelming outcome on Saturday. Nonetheless, they have now kept a clean sheet in three successive matches.
While Slovan's 2022-23 title triumph was secured by a margin of just two points, Tuesday's visitors won their domestic league by a country mile - scoring more goals and conceding fewer than any other team to claim first place by 20 points from runners-up Borac Banja Luka.
Krunoslav Rendulic's side returned to competitive action this summer by progressing from a Champions League qualifier for the first time in club history, as Armenian outfit Urartu were beaten on penalties after the teams' first-round contest had ended level on aggregate.
Following their defeat last week, though, the Bosnian champions have now won only three of 17 qualifying games in Europe's top club competition while scoring just nine times in the process - although they did reach the Conference League playoffs this time last year.
On that occasion, Zrinjski were turfed out just short of the group phase by none other than Slovan Bratislava - losing 6-5 in a dramatic spot-kick shootout - so they will be doubly determined not to suffer a similar fate this week.
Slovan Bratislava Champions League form:
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W
W
Slovan Bratislava form (all competitions):
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L
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D
Zrinjski Mostar Champions League form:
W
W
L
Zrinjski Mostar form (all competitions):
D
W
L
W
W
L
Team News
Vladimir Weiss made several changes to his Slovan Bratislava XI for Saturday's draw with Kosice, as Cesar Blackman and Kevin Wimmer were among those returning to the side.
Ghanaian striker Malik Abubakari and veteran midfielder Juraj Kucka were also promoted to the starting lineup, but Aleksandar Cavric is now likely to replace the former and Armenian winger Tigran Barseghyan could come in for the latter.
Despite strong competition from Nemanja Bilbija, Zrinjski Mostar should turn to Tomislav Kis to lead their attack in Slovakia. The well-travelled striker - who has spent time in Belgium, China and Hungary in the past - scored a crucial extra-time goal which helped Zrinjski set up a successful penalty shootout in the first qualifying round.
Having recently made his move from Dinamo Zagreb permanent after scoring eight goals on loan last term, Mario Cuze provides support from the left flank; meanwhile, Bosnia international Hrvoje Barisic captains the visitors from the heart of their back four.
Slovan Bratislava possible starting lineup:
Borjan; Pauschek, Kashia, Wimmer, Lovat; Kankava, Savvidis; Barseghyan, Tolic, Zuberu; Cavric
Zrinjski Mostar possible starting lineup:
Maric; Corluka, Senic, Barisic, Memija; Stanic, Canadjija; Ticinovic, Ivancic, Cuze; Kis
We say: Slovan Bratislava 1-0 Zrinjski Mostar (Slovan Bratislava win 2-0 on aggregate)
With an impressive recent record of keeping clean sheets, Slovan Bratislava can defend their lead and perhaps even extend it; sealing progress to the third round. So for the second year running, Zrinjski will see their European adventure ended by Slovakia's most successful club.