Chicago Fire midfielder Przemysław Frankowski, who came in as a second-half substitute, scored the 1-0 lead for Poland from close range, after being assisted by captain Robert Lewandowski, in the 74th minute of play at the National Stadium in the Polish capital.
Substitute striker Arkadiusz Milik put the score at 2-0 with a left-footed blast from outside the box after an assist by Lewandowski in the 80th minute.
After eight rounds of fixtures, Poland are on top of their qualifying group G, with 19 points, three more than Austria.
The top two teams from each group qualify directly for the championships.
The Poles will face off against Israel and Slovenia in their last two qualifying fixtures in November.
The Polish team on Thursday beat Latvia 3-0 in its seventh Euro 2020 qualifier, with three goals from Lewandowski in an away game in Riga.
Poland opened their Euro 2020 qualifying campaign with a 1-0 away win against Austria on March 21. The Polish team three days later beat Latvia 2-0 in their second Euro 2020 qualifier at the National Stadium in Warsaw.
Poland on June 7 beat North Macedonia 1-0 at Toše Proeski Arena in the Balkan country’s capital Skopje. Three days later Jerzy Brzęczek's men demolished Israel 4-0 at home in their fourth straight Euro 2020 qualifying win.
The Poles on September 6 lost 0-2 to lower-ranked Slovenia after an uninspiring performance at Stožice Stadium in Ljubljana. Three days later they tied 0-0 with Austria at the National Stadium in Warsaw.
Fifty-five European teams were in December drawn into a total of 10 qualifying groups, five groups of five teams and five six-team groups.
The Euro 2020 qualifiers will be played until November, with the top two teams from each group advancing directly to the championships.
The Euro 2020 tournament will be held from June 12 to July 12, 2020 in 12 cities around Europe, with the final played at London's Wembley Stadium.
Brzęczek took over as Poland manager last summer after the national squad’s early exit from the World Cup in Russia.
Poland in 2016 made it through to the quarterfinals of the European championships in France, losing to Portugal on penalties.
Source: Polsat Sport