Sebastian Szymański and Adam Buksa scored for Poland against the 10-man hosts at Gundadalur Stadium in Tórshavn, the capital of the Faroe Islands, on Thursday night.
The match marked a successful debut for Poland's new coach Michał Probierz, who replaced Portugal's Fernando Santos last month.
The victory came after the Polish team's bitter 0-2 defeat to Albania in its previous qualifier last month.
Poland are ranked 30th worldwide by football's governing body FIFA, while the Faroe Islands are No. 131 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 then beat Albania 1-0 at home in their second qualifier on March 27. Poland in June lost 2-3 to Moldova in their third Euro 2024 qualifier in Chișinău.
Poland beat the Faroe Islands 2-0 in their fourth Euro 2024 qualifier in Warsaw on September 7.
Poland on September 10 lost 0-2 to Albania in their fifth Euro 2024 qualifier in Tirana, leaving fans jittery about the team's chances of qualifying for the European tournament next year.
After six rounds of fixtures, Poland are second in their qualifying Group E, with nine points, behind Albania on 13 points, having played one match more than the Czech Republic and Moldova.
The Poles take on Moldova at home in their next qualifier on Sunday, October 15.
(gs)
Source: IAR, PAP