Substitute striker Karol Świderski scored the only goal of the match in the 77th minute at the Arena Kombëtare stadium in Tirana, after being set up by midfielder Mateusz Klich.
The game was temporarily halted after bottles were thrown on the pitch from the crowd in the second half.
The Poles, under their Portuguese manager Paulo Sousa, are ranked 24th worldwide by football's governing body FIFA, while Albania are No. 66 in the FIFA table.
After eight rounds of fixtures, Poland are in second place in their qualifying Group I, behind England, with 17 points and a plus-17 goal differential.
Poland needed to beat Albania or at least earn a draw on Tuesday night to preserve their chances of qualifying for next year's World Cup in Qatar.
The Polish team, captained by star striker Robert Lewandowski, FIFA's world player of the year for 2020, on October 9 demolished underdogs San Marino 5-0 in its previous 2022 World Cup qualifier.
The Poles will now take on Andorra in their next World Cup qualifying fixture away from home on November 12.
The qualification stage for the 2022 World Cup runs until next month, while the tournament will be held in Qatar from November 21 to December 18, 2022.
Source: TVP, PAP