The goals for the Polish team came from Przemysław Frankowski, Piotr Zieliński, Jakub Piotrowski and Sebastian Szymański, in addition to an own goal from Estonia's Karol Mets.
Martin Vetkal scored a consolation for Estonia in the 78th minute of the game at Warsaw's National Stadium on Thursday night.
Poland will now take on Wales in an away playoff final on Tuesday, March 26.
The winner of the match will secure a spot in Euro 2024, which kicks off in Germany in mid-June.
A total of 12 teams are vying for the three remaining Euro 2024 spots in two-stage, single-leg playoffs this month.
The winners of the three playoff paths will complete the 24-team Euro 2024 lineup, joining 20 teams that advanced from the 10 qualifying groups plus hosts Germany, European football's governing body UEFA has said.
Poland missed out on a chance to qualify directly for Euro 2024, after drawing 1-1 with the Czech Republic in their last qualifying game in Warsaw in November.
Poland won 11 points from eight matches in their qualifying Group E, which also included Albania, Moldova and the Faroe Islands.
The Euro 2024 tournament will be held from June 14 to July 14 in 10 cities in Germany, with the final played at Berlin's Olympiastadion.
The Poles, captained by star striker Robert Lewandowski, are ranked 30th worldwide by football's governing body FIFA, while Wales are No. 29 in the FIFA table.
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Source: IAR, PAP