Striker Ewa Pajor opened the scoring in the 15th minute, but Sofija Krajsumovic equalised for the visitors in the 40th, Polish state news agency PAP reported.
Pajor restored Poland's lead early in the second half with a close-range finish, and Adriana Achcińska made it 3-1 just two minutes later after a goalkeeper error.
Klaudia Słowińska added a fourth goal for Poland in the 77th minute, capitalising on a defensive lapse, and Martyna Wiankowska sealed the win with a penalty in the 89th.
The home victory in the Baltic city of Gdańsk marked Poland's third straight Nations League win, following a 2-0 triumph over Northern Ireland and a 1-0 win against Romania.
Poland, the top seeds in League B Group 1, are ranked 28th in the world by football's governing body FIFA, while Bosnia and Herzegovina are No. 62 in the FIFA table.
Manager Nina Patalon's squad will take on Bosnia and Herzegovina away on Tuesday in their next Nations League fixture.
Later this year, Poland will join 15 other teams from across Europe for the Euro 2025 tournament in Switzerland.
Poland have been drawn to play Germany, Sweden and Denmark in the group stage of this year's European football championships.
Poland head coach Nina Patalon. Photo: PAP/Adam Warżawa
The Polish team opens its Euro 2025 campaign against Germany on July 4.
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Source: IAR, PAP, pzpn.pl