The match kicked off at 8:45 p.m. Warsaw time in the Croatian city of Osijek.
The game remained goalless through the first half, with Croatia's Luka Modrić making a decisive impact in the 52nd minute, when he scored the only goal of the match from a free kick.
The Poles were captained by star striker Robert Lewandowski.
Poland had opened their campaign on Thursday with a 3-2 victory over Scotland in Glasgow, following goals from Sebastian Szymański, Robert Lewandowski and Nicola Zalewski.
Croatia, meanwhile, had lost their opening Nations League game 1-2 away to Portugal.
Poland is ranked 28th worldwide by football's governing body FIFA, while Croatia is 12th in the FIFA rankings.
Michał Probierz's men have been drawn to play Scotland, Croatia and Portugal in the group stage of the 2024/2025 UEFA Nations League.
The four teams will play one another home and away in Group 1 of League A from September to November.
The Nations League is UEFA’s newest national-team competition, now in its fourth edition.
(ał)
Source: PAP, IAR