They would need Colombia to beat Peru or Peru to beat Colombia by two clear goals, coupled with either Chile losing by two clear goals against Brazil or Paraguay failing to win at home to Venezuela. Man for man Argentina arguably has the most talented squad of players in the global game.
Brazil, who have already secured their place in Russian Federation, were held to a 0-0 draw by Bolivia in La Paz, while Colombia missed out on securing a World Cup spot after losing 2-1 at home to Paraguay.
"I am still confident that we will be at the World Cup".
"I never saw such disappointment in a dressing room; several of my team-mates were crying and Adolfo Pedernera [Argentina's coach] was sat silently in a corner smoking", Argentine player Alberto Rendo told FIFA.com.
So tight is the group that four points separate Uruguay in second (28) and Paraguay (24) in seventh and a win for Argentina could see them qualify automatically. Their win shoots them up from sixth to third and places their World Cup fate in their own hands.
Now sitting top of Group B, a home victory against nearest rivals Zambia - who sit just three points behind - would guarantee qualification to Russian Federation 2018.
Can Argentina make it through to the World Cup?
Earlier, group leaders Brazil and ninth-placed Bolivia played out a goalless draw in a match that had no bearing on the final standings.
Cue the mother of all slices as Messi completely shanked his effort out to the left with so much spin that it ended in a Peru throw-in. But Messis Argentina barely shoots goals: whole 16 in so far 17 games. "We love you forever and ever". We are going to play against an important national team in a big venue but it's no different to what we have had to encounter in previous games.
Alexis Sanchez's late victor for Chile, coupled with Paraguay snatching an injury-time victor in Barranquilla, means the Albiceleste are now sixth in the table, outside the qualification places, and need other results to favor them in the final round of fixtures if they are to qualify automatically.
The coach said in a news conference: "We don't generally man-mark players".