Star striker Robert Lewandowski scored both goals in the second half, Polish state news agency PAP reported.
The Barcelona forward opened the scoring from the penalty spot on 73 minutes, before making it 2:0 ten minutes later, according to news outlets.
The Polish team, coached by Portuguese manager Fernando Santos, bounced back from a shock 2-3 defeat to Moldova in its previous qualifier in Chișinău in June.
Poland are ranked 26th worldwide by football's governing body FIFA, while the Faroe Islands are No. 129 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.
After four rounds of fixtures, Poland are third in their qualifying Group E, with six points after two wins and two defeats.
The Czech Republic top the group on eight points, followed by Albania on seven, European football’s governing body UEFA said.
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.
Poland failed to get past the group stage at the postponed Euro 2020 tournament, where they suffered a defeat to Slovakia before drawing with Spain and losing the decisive game against Sweden.
The Polish team made it through to the quarterfinals of the Euro 2016 championships in France, losing to Portugal on penalties.
Poland reached the last 16 of last year's World Cup in Qatar before being eliminated by eventual runners-up France.
Portugal's Santos took over as Poland manager in January.
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Source: PAP, TVP Sport, UEFA
