Captain Robert Lewandowski opened the scoring for Poland with a clinical header after a set piece 12 minutes into the game at the National Stadium in Warsaw.
Sokol Cikalleshi equalised for Albania with a precise finish from inside the box 13 minutes later.
New England Revolution striker Adam Buksa put Poland 2-1 ahead in the 44th minute on his debut with the national team after being set up by former Chicago Fire midfielder Przemysław Frankowski.
Defensive midfielder Grzegorz Krychowiak extended Poland’s lead after scoring the team's third goal from close range in the 54th minute before substitute midfielder Karol Linetty set the final score at 4-1 for the home team in the 89th minute.
The Poles, under their Portuguese manager Paulo Sousa, went into the match missing several key players who had been ruled out by injuries.
Meanwhile, the squad's Leeds United midfielder Mateusz Klich was unavailable for duty after testing positive for the coronavirus.
Poland are ranked 27th worldwide by football's governing body FIFA, while Albania are No. 69 in the FIFA table.
The Poles will now take on San Marino in their next World Cup qualifying fixture away in Serravalle on Sunday.
The Polish team opened its 2022 World Cup qualifying campaign with a 3-3 away draw with Hungary in Budapest on March 25.
The Poles, captained by Robert Lewandowski, FIFA's world player of the year for 2020, beat Andorra 3-0 in their second World Cup qualifier at home on March 28.
Poland in late March lost 1-2 to England in their third 2022 World Cup qualifier in London.
With Poland’s victory over Albania and England’s 4-0 win over Hungary on Thursday, Poland now sits in second place of its qualifying Group I with seven points and a plus-five goal differential.
The qualification stage for the 2022 World Cup runs until November 2021, while the tournament will be held in Qatar from November 21 to December 18, 2022.
(gs)
Source: TVP Sport, PAP