The Azzurri will reach the finals if they win - or even if they draw and the Netherlands fail to beat Poland. While even with what would be a historic win, Bosnia cannot avoid the trapdoor to League B.
As Italy head coach Roberto Mancini is still in quarantine, his assistant Alberigo Evani must continue to helm a slimmed-down squad, which initially comprised a bloated 41 names, in the Bosnian capital.
Evani has so far overseen a 4-0 friendly win against Estonia - featuring at best a 'B' team - and an excellent 2-0 Nations League triumph over Poland which took the Azzurri top of a challenging group.
The former Milan and Sampdoria player, who had been part of the Azzurrini youth setup for almost a decade, will now aim to stretch Italy's unbeaten run to six consecutive games in the continent's newest competition.
They have continued to demonstrate an impressive solidity throughout the campaign, conceding just two goals in five matches - this coming despite Mancini's avowed commitment to attack.
Even in the absence of a whole raft of first-choice defenders and chief goal threat Ciro Immobile - currently at the centre of COVID-19 controversy - Italy kept a clean sheet against a Poland side featuring Robert Lewandowski and, in fact, they did not even concede a single shot on target at Sassuolo's Mapei Stadium.
Registering 19 shots and 62% of possession in what was, to some extent, a group decider demonstrates that - even in trying circumstances, without their manager and key players - the Italians have forged a winning mentality.
In diametric opposition, Bosnia-Herzegovina coach Dusan Bajevic has failed to win any of his opening seven matches in charge and the one-time international overachievers only have one victory - away to lowly Liechtenstein - to show from their last ten outings.
After their Euro 2020 playoff semi-final defeat at the hands of Northern Ireland, things have gone from bad to worse for Bajevic's side, as they twice conceded three goals in consecutive defeats to Poland and the Netherlands.
Losing on penalties to Ian Baraclough's similarly-struggling side was a dagger blow to the confidence of a squad which had actually opened its Nations League campaign with an impressive 1-1 draw away to this Wednesday's opponents.
National hero, Roma striker Edin Dzeko, gave the visitors the lead in that contest - the nations' first encounter in Sarajevo since they met for the first time ever in a 1996 friendly. That celebrated occasion brought the Bosnians' only win against the Azzurri to date - an unlikely feat which they will only hope, rather than expect, to repeat this time around.
Bosnia-Herzegovina Nations League form: DLDLL
Bosnia-Herzegovina form (all competitions): LDDLLL
Italy Nations League form: DWDDW
Italy form (all competitions): WWDDWW
Bosnia will again be without the services of talismanic forward Edin Dzeko due to his ongoing self-isolation in Rome - though he still hopes to return to Serie A action at the weekend.
Armin Hodzic, on loan at Kasimpasa, deputised for Dzeko on Sunday, though Eupen striker Smail Prevljak could earn a start following his impressive showing off the bench last time out, scoring the consolation goal against the Netherlands. Centre-back Anel Ahmedhodzic is available again after suspension and will contend for a start.
Dusan Bajevic's team is particularly strong in midfield, where Edin Visca and Amer Gojak occupy the wide roles, while Barcelona's Miralem Pjanic and AC Milan man Rade Krunic will operate centrally in a flexible 4-1-4-1 formation.
Italy are without central defenders Leonardo Bonucci, Giorgio Chiellini, Alessio Romagnoli and Angelo Ogbonna due to injury, with Alessandro Bastoni being promoted from the Under-21s to feature in last week's matches. Danilo D'Ambrosio could be drafted in for Bastoni, to reduce his Inter team-mate's workload.
Forwards Vincenzo Grifo and Moise Kean have returned to their respective clubs following minor injuries, so Torino's Andrea Belotti is expected to keep the central striker's spot, with support from two of Lorenzo Insigne, Stephan El Shaarawy and Federico Bernardeschi.
Bosnia-Herzegovina possible starting lineup:
Sehic; Cipetic, Ahmedhodzic, Sanicanin, Kolasinac; Cimirot; Visca, Pjanic, Krunic, Gojak; Hodzic
Italy possible starting lineup:
Donnarumma; Calabria, D'Ambrosio, Acerbi, Emerson; Tonali, Jorginho, Barella; El Shaarawy, Belotti, Insigne
We say: Bosnia-Herzegovina 0-2 Italy
Italy's need for points is greater, with top spot in the group and potential Nations League final stage matches in Turin and Milan up for grabs. The hosts, meanwhile, are merely playing for pride, without the considerable presence of their star man Dzeko.
Therefore, expect the Azzurri - unbeaten in 21 games now - to make full use of their growing squad depth in order to edge past dogged but slightly dispirited opponents, who simply cannot wait for 2020 to end.