Captain Robert Lewandowski opened the scoring for the home team from a penalty in the 49th minute at the Silesian Stadium in the southern Polish city of Chorzów.
Midfielder Piotr Zieliński made it 2-0 for Poland after an error by the away team's defence in the 72nd minute, sealing the win and sending fans into jubilation.
Polish football players celebrate after the final whistle on Tuesday night. Photo: PAP/Łukasz Gągulski
The Poles, under manager Czesław Michniewicz, went into the match ranked 28th worldwide by football's governing body FIFA, while Sweden were No. 17 in the FIFA table.
Football’s world governing body FIFA earlier this month banned Russia from the playoffs for the World Cup in Qatar, giving Poland a bye to the playoff finals in European qualifying for the World Cup.
The 2022 World Cup will be held in Qatar from November 21 to December 18.