Second-half goals from Julian Alvarez and Alexis Mac Allister secured qualification for Argentina, after they won 2-0 to leapfrog Poland and top Group C in Doha.
Brighton man Mac Allister got on the end of a Nahuel Molina cross just after half-time to ease Argentinian nerves regarding qualification, before Alvarez secured the points on 67 minutes with a stunning strike into the top-right corner.
However, it could have all been so much different for La Albiceleste.
Their star man Lionel Messi won a penalty minutes before the break but saw his effort from the spot denied by Wojciech Szczesny.
The penalty save was still whilst Mexico and Saudi Arabia were held at 0-0 but had Mac Allister not made amends for Messi, Argentina could have been eliminated from the World Cup at the group stage.
A loss in Doha left Poland's destiny out of their hands, with Czesław Michniewicz's side only through on disciplinary points.
However, after the final whistle, Saudi Arabia scored a consolation to confirm Poland's chance to go up against France in the Round of 16.
Story of the match
A raucous atmosphere from the Argentinian contingent inside Stadium 974 laid the backdrop to La Albiceleste's must-win match and they would go closest first.
Marcus Acuna had two early chances for his country.
The Sevilla man first brought down Messi's lofted ball out to the left-wing, before cutting inside the defender but blazing his right-footed shot high and wide.
But he would get another chance.
Manchester City's Julian Alvarez had his shot parried by Szczesny to the edge pf the area, where Acuna drilled it back towards goal, only to see his effort fly inches past the post.
Argentina's dominance in the first period continued and almost paid dividends in bizarre fashion.
Juventus' Angel Di Maria swung a corner right on top of Szczesny's head but his Bianconeri teammate was able to tip the ball just over the crossbar.
Szczesny was crucial to Poland's first-half survival and he made himself a penalty hero for his side in Qatar again.
Alexis Mac Allister released Alvarez in behind but the Man City forward saw his shot parried by the Polish goalkeeper, only for Szczesny to be penalised controversially for his collision on the follow-up with Messi.
However, when faced with the PSG man from 12 yards, Szczesny was unfazed, stopping Messi's effort with a strong right hand to keep the scores level.
Mac Allister makes the difference
Poland defended valiantly for the first 45 minutes, but just seconds into the second half their efforts were to be in vain.
Di Maria and Nahuel Molina combined down the right-hand side, before the latter found Mac Allister in the area, allowing the Brighton man to sweep home and give Argentina the lead.
On the hour mark, Mac Allister could and perhaps should have doubled his tally and his side's lead.
A low ball across the box from the left-hand side missed every attacker and defender waiting to meet it but, unfortunately for him, he scuffed his shot straight into the gloves of Szczesny.
Where Mac Allister was unable to double the lead, though, Alvarez more than made up.
Full debutant Enzo Fernandez poked through the Man City forward, who worked the angle for a shot into the top-right corner to send the travelling Argentinians in Doha wild.
Due to Mexico winning 2-0 against Saudi Arabia, Poland were extraordinarily only in the tournament on greater disciplinary points with 20 minutes left to go.
But the bureaucracy of obscure FIFA rules and was almost avoided when Argentina substitute Nicolas Tagliafico beat Szczesny with a clever chip.
However, the Benfica full-back did not beat the Polish defence, with Glik heading off the line to keep his country in the World Cup by the skin of their teeth.
Despite that, the discussion of disciplinary records and drawing of lots was to be in vain.
Following the whistle in Doha, the Green Falcons scored a crucial consolation against Mexico, to guarantee Poland's qualification.
Player of the match
Wojciech Szczesny
The Juventus goalkeeper made himself a Polish World Cup hero with his first penalty save of the group stage against Saudi Arabia, as his side came away with the points.
In Doha, he made himself the hero from 12 yards again and then some.
With Poland qualifying on goal difference, Szczesny has to take the plaudits despite the loss at Stadium 974.
Making 9 saves and earning a match rating of 8.5, as per WhoScored, there can be no doubt that had the Juve shot stopper not been in the Polish net, Mexico would have been facing France in the Round of 16.
Lineups
Poland XI: Szczesny (GK), Cash, Glik. Kiwior, Bereszynski, Zielinski, Bielik, Krychowiak, Frankowski, Swiderski, Lewandowski
Argentina XI: Martinez (GK), Molina, Romero, Otamendi, Acuna, De Paul, Fernandez, Di Maria, Messi, Mac Allister, Alvarez