Striker Karol Świderski scored the only goal of the match in the 41st minute at the National Stadium in Warsaw.
Poland opened their Euro 2024 qualifying campaign with a 1-3 defeat against the Czech Republic on March 24.
After two rounds of fixtures, Poland were second in their qualifying Group E, which also includes Moldova and the Faroe Islands.
The Poles, captained by star striker Robert Lewandowski and coached by Portuguese manager Fernando Santos, take on Moldova away from home in their next qualifier on June 20.
Fifty-three teams were in October drawn into a total of 10 qualifying groups, seven groups of five teams and three six-team groups.
Euro 2024 qualifiers will be played until November this year, with the top two teams from each group qualifying directly for the championships.
The Euro 2024 tournament will be held from June 14 to July 14, 2024 in 10 cities in Germany, with the final played at Berlin's Olympiastadion.
Source: IAR, PAP, Polsat Sport