While the hosts were thumped by Germany, their visitors lost an eventful seven-goal contest with the Netherlands.
Match preview
Just weeks after being beaten by their German counterparts at Euro 2024, Hungary found themselves on the wrong side of the result again on Saturday evening, when they were handed a 5-0 drubbing in Dusseldorf.
Conceding four times during the second half - in a game that also saw their hosts strike the crossbar twice - consigned Marco Rossi's men to a humbling first-day defeat in Group 3.
Heading into the Euros, Hungary had lost just once in 16 matches, pushing Italy for a place in the most recent Nations League finals before coming up just one point short in a group also featuring Germany and England.
However, the Magyars have now come away empty-handed from three of their last four games, conceding 10 goals in the process - and if that form continues they face relegation from League A.
Though a top-two finish would secure entry to the Nations League's new quarter-final stage, third place would result in a survival playoff, and fourth means automatic demotion; therefore, they cannot afford a home loss on Tuesday.
While their upcoming opponents - and likely competitiors for third spot in Group 3 - had no answers to Germany's excellence, Bosnia-Herzegovina put up much more of a fight against the Netherlands, but ultimately to no avail.
After going behind to Joshua Zirkzee's 13th-minute header, Bosnia bit back through a Ermedin Demirovic equaliser, before finding themselves 3-1 down at the hour mark.
Captain and talisman Edin Dzeko notched his 66th international goal to tighten matters up again, but the hosts eventually ran out 5-2 winners in Eindhoven, as Bosnia suffered defeat on their debut at the Nations League's elite level.
Having beaten Finland, Montenegro and Romania to first place in League B last time around, the Dragons are now mixing it with some of Europe's heavyweights.
Though that Nations League performance earned them a place in the Euro 2024 playoffs, they were then beaten by Ukraine, leading to the swift exit of former boss Savo Milosevic.
New coach Sergej Barbarez has since overseen three straight defeats: to Italy and England in friendlies, then Saturday's setback in the Netherlands. In fact, Bosnia have now lost their last seven games, dating back to October of last year.
Hungary Nations League form:
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Bosnia-Herzegovina Nations League form:
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Team News
While Marco Rossi may be pondering changes after his side's heavy defeat in Germany, one certain selection is captain Dominik Szoboszlai, while goalkeeper Peter Gulacsi and centre-back Willi Orban are also fixtures in the starting XI.
Barnabas Varga returned to lead Hungary's attack on Saturday, having recovered from the head injury he sustained against Scotland at the Euros, and he should again see off competition from Martin Adam to feature up front.
Rossi was ruthless following the Magyars' Euros exit, and Laszlo Kleinheisler, Adam Lang, Callum Styles and Atilla Szalai were all dropped from the squad for this month's matches.
Meanwhile, Bosnia's front line will be led by veteran striker Edin Dzeko, who scored on his 135th international appearance at the weekend, but many of his teammates have yet to reach double figures for senior caps.
Three men made their competitive debut in Eindhoven, and Sergej Barbarez is set to keep faith with his youthful side on Tuesday night.
Two of the visitors' top defenders - Anel Ahmedhodzic and Sead Kolasinac - withdrew due to injury, so FC Zurich's Nikola Katic could helm a makeshift back five.
Hungary possible starting lineup:
Gulacsi; Balogh, Orban, M. Dardai; Bolla, A. Nagy, Schafer, Kerkez; Sallai, Szoboszlai; Varga
Bosnia-Herzegovina possible starting lineup:
Vasilj; Gazibegovic, Mujakic, Katic, Bicakcic, Dedic; Gigovic, Krunic, Tahirovic; Demirovic, Dzeko
We say: Hungary 2-1 Bosnia-Herzegovina
Hungary may have stumbled against tough opposition - losing twice to Germany and once to Switzerland since the start of the Euros - but they are hard to beat on home turf and should bounce straight back from Saturday's defeat.