The two-time world champions had to rely on superstar Lionel Messi to keep their qualification hopes alive following their stunning 2-1 defeat at the hands of low-ranked Saudi Arabia.
He masterminded a victory 2-0 over Mexico, scoring their first goal with a superb finish to put their campaign back on track.
The brilliant Argentine, whose team are one of the tournament favourites, is playing his fifth and final campaign, meaning it is his last chance to match the late Diego Maradona and lift the biggest trophy of the sport.
"Everything comes down to details," Argentina defender Lisandro Martinez said on Tuesday. "We saw it with Messi's goal. Before that the match (against Mexico) was very tight.
"We know what we are capable of. We can play better and we know we have not reached our best level yet. But we are trying."
With Argentina second in Group C on three points, one behind the Poles, they must win to be sure of progressing.
A draw could potentially also be enough for the South Americans too if Mexico and Saudi Arabia also end level.
Unlike their previous group matches, they will come up against a stronger frontline led by Poland's own big-name forward Robert Lewandowski.
"We have to be well organised so they don't get us on the counter-attack," Martinez said.
Like Messi, Lewandowski is also his nation's all-time top scorer, on possibly his last mission at a World Cup.
He uncharacteristically missed a penalty in Poland's opening draw with Mexico before scoring his first ever World Cup goal in their 2-0 win over Saudi Arabia.
"He is a top player and it will be a privilege and pleasure to see him from up close as a football fan," Argentina coach Lionel Scaloni said. "Is he at the same level as Messi? You just have to enjoy such a good player. Why compare one player with another. That's not helpful."
Scaloni said their stuttering World Cup campaign was now in the past and all that mattered was the match against Poland and a spot in the last 16.
"For us the most important game is the one we are about to play. Whatever happened is in the past and remains there."
