La Albiceleste incredibly lost their competition opener to Saudi Arabia, but they have now beaten Mexico and Poland in Group C to progress to the knockout round of the tournament as section winners.
Alexis Mac Allister and Julian Alvarez scored the goals for Argentina, who will take on Group D runners-up Australia in the next round on Saturday.
Lionel Messi missed a first-half penalty for Lionel Scaloni’s side, but the South Americans scored twice without reply in the second half of the contest to secure first position in the group.
Poland, meanwhile, have progressed to the next round ahead of Mexico, with Czeslaw Michniewicz’s side set to face the holders France on Sunday.
Disciplinary points were separating Poland and Mexico until Saudi Arabia found the back of the net in second-half stoppage time against Mexico to suffer a 2-1 defeat.
Nicolas Otamendi had an early half-chance for Argentina at the far post, but his header was always dropping wide of the target.
Messi’s first sight of the Poland goal then came in the seventh minute when he worked some space outside the box, but the Paris Saint-Germain attacker’s effort was straight at Wojciech Szczesny.
The Poland goalkeeper had to deny Messi again in the 10th minute, with the Argentina captain making a strong start to the contest, before Marcos Acuna fired over the Poland crossbar seven minutes later.
Acuna was heavily involved down the left, with the defender heading just wide of the target following more good work from Messi in an advanced area.
Acuna again tried his luck in the 29th minute, firing a powerful effort wide of the post, before Szczesny tipped a clever Angel Di Maria corner over the crossbar three minutes later.
Enzo Fernandez placed one over the crossbar 10 minutes before the end of the first period, before the Poland goalkeeper made another smart save to keep out a close-range effort from Alvarez.
There was then a VAR review to look at a challenge from Szczesny on Messi, with the stopper catching the PSG attacker with his arm as both players attempted to make contact on a cross, and the referee decided to point to the spot after a long look at the monitor.
Messi stepped forward, but it was a terrific save from the Juventus goalkeeper, who guessed the right way and got a strong hand to the ball.
Di Maria should have made contact on a low cross from Messi in the spell of pressure that followed, before Szczesny saved from Alvarez and then Di Maria, with Poland struggling to get out of their own half.
Argentina finally made the breakthrough early in the second half, though, with Mac Allister cleverly turning a cross from Nahuel Molina into the bottom corner of the net.
Poland had a chance to level in the 49th minute when Kamil Glik climbed highest inside the Argentine box to meet a deep cross, but the centre-back’s header was just wide of the post.
Mac Allister then brought a smart save from the Poland goalkeeper just past the hour after excellent work from Messi had released the Brighton & Hove Albion attacker.
Alvarez doubled Argentina’s advantage in the 68th minute, with the Manchester City forward picking out the top corner of the net after finding space inside the Poland box.
Szczesny did well to deny Messi 20 minutes from time, before Alvarez hit the side netting after being released by Messi three minutes later.
Lautaro Martinez had a brilliant chance to make it 3-0 to Argentina in the 85th minute when he broke into the Poland box, but the Inter Milan forward missed the target.
Nicolas Tagliafico then had one cleared off the line in the final moments, with Jakub Kiwior the saviour for Poland, who had fewer yellow cards than Mexico in the group stage, which looked to be the difference until Saudi Arabia found the back of the net against Mexico late on to mean that goal difference came into play.