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Talisman Lewandowski's penalty failure against Mexico had denied Poland an opening win, but he and they made amends at Education City Stadium, toppling Argentina's conqueror to blow Group C wide open.
Although Saudi Arabia was largely more impressive than in its smash-and-grab defeat of Argentina, it again fell behind and this time could not recover – the latest episode of spot-kick drama making a hero of Wojciech Szczesny after he denied Salem Al Dawsari.
Either side of that save, Lewandowski assisted the opening goal for Piotr Zielinski and belatedly netted a breakthrough strike to make sure of a win that moves Poland to four points ahead of its clash with Argentina.
Matty Cash raced onto an incisive pass six minutes before the break and squared to Lewandowski, whose first touch took him away from goal before he cut the ball back for Zielinski's clinical finish.
The response might have been swift as a VAR review granted Saleh Al Shehri a soft penalty following contact from Krystian Bielik, but Szczesny sensationally repelled Al Dawsari's spot-kick and then – even more spectacularly – Mohammed Al Burayk's follow-up.
Szczesny had to come to Poland's rescue again 10 minutes after the restart, blocking with his legs from Al Dawsari, and Feras Al Brikan and Mohammed Kanno each blazed wildly off target.
Poland squandered chances to put the game to bed as first Arkadiusz Milik and then Lewandowski worked the frame of the goal, but the Barcelona man eventually got his goal after pinching possession from Abdulelah Al Malki and finishing calmly.