Lionel Messi guided his side to win the group after their 2-0 win over Robert Lewandowski’s side on Wednesday.
They finished the group with six points, more than anyone else.
Poland finished equal on points with Mexico (4), but go ahead on goal difference – having conceded fewer goals in the group stages.
Argentina will face Australia in the Round of 16 on Saturday, 3 December. Lewandowski’s side face defending champions France on Sunday, 4 December.
Lewa had a frustrating outing against Argentina, not having a shot on target and only completing 11 passes. Messi also had a penalty saved by Wojciech Szczesny.