The defeat came a day after FIFA announced it was investigating possible match-fixing in Argentina's 4-1 defeat in Nigeria last Wednesday when both sides were awarded controversial penalties.
Coach Sergio Batista, fielding European-based players on the fringes of the first-choice squad, has also been criticised by Argentina FA president Julio Grondona, who said the team's prestige was being put at risk.
Substitute Pawel Brozek scored the winner in the 67th minute as Poland, like Nigeria, made their greater pace in attack pay while the Argentines generally failed to impose the possession game Batista preaches.
Midfielder Adrian Mierzejewski gave the home side the lead midway through the first half, easily slipping past a defender and giving keeper Adrian Gabbarini no chance.
Argentina's best move less than two minutes into the second half led to striker Marco Ruben equalising when he turned in the box on the right to send a diagonal shot into the bottom far side of the Wojciech Szczesny's net.
Argentina are preparing to host the Copa America next month but only two players in the tour party were included in the 26-man provisional tournament squad named by Batista on Tuesday.
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