Striker Arkadiusz Milik put Poland 1-0 ahead from close range 12 minutes into the game at Zimbru Stadium in the Moldovan capital, and captain Robert Lewandowski added another goal from outside the box 22 minutes later.
But Ion Nicolaescu scored for Moldova in the 48th minute and then put the hosts level at 2-2 in the 79th.
Vladislav Baboglo set the final score at 3-2 for the home team with a header in the 85th minute.
Poland are ranked 23rd worldwide by football's governing body FIFA, while Moldova are No. 171 in the FIFA table.
The Polish team on March 24 opened its Euro 2024 qualifying campaign with a 1-3 defeat against the Czech Republic. The Poles beat Albania 1-0 at home in their second Euro 2024 qualifier on March 27.
After three rounds of fixtures, Poland are fourth in their qualifying Group E, which also includes the Faroe Islands.
The Poles, coached by Portuguese manager Fernando Santos, take on the Faroe Islands at home in their next qualifier on September 7.
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.
(gs)
Source: IAR, PAP, TVP Sport