The South Americans were narrowly beaten by Italy in their opening game, while South Africa were edged out by Sweden.
Match preview
After failing to progress from the group stages in all of their previous three World Cup appearances, Argentina's hopes of reaching the knockout stages for the first time were dealt a blow in their tournament opener.
Their Matchday one meeting with Italy looked set to finish goalless, before an 87th-minute from Cristian Girelli condemned La Albiceleste to a 1-0 defeat.
Argentina are still left waiting for their first win at the World Cup finals, with their 10 games at the tournament producing two draws and eight defeats.
They will at least be able to take confidence from their recent defensive performances, having conceded just two goals in their last seven internationals.
With Argentina ranked 26 places higher than South Africa in the FIFA World Rankings, they will certainly go into Friday's contest as the favourites.
South Africa have already demonstrated that they will be no pushover after running Sweden close in Sunday's narrow 2-1 defeat.
Hildah Magaia opened the scoring for South Africa just after half time, before Fridolina Rolfo restored parity in the 65th minute.
The Banyana Banyana went agonisingly close to picking up a point, but Amanda Ilestedt's 90th-minute winner ensured they were left empty-handed.
After producing an impressive performance against the second-highest ranked team in the world, South Africa will believe that they can trouble Argentina and Italy in their final two group games.
Having lost all four of their games at the World Cup finals, South Africa will be looking to claim their first points at the tournament on Thursday.
Argentina Women Women's World Cup form:
L
Argentina Women form (all competitions):
South Africa Women Women's World Cup form:
L
South Africa Women form (all competitions):
Team News
Despite falling to defeat in their opening game, Argentina boss German Portanova could decide to name an unchanged starting XI.
After picking up yellow cards against Italy, Miriam Mayorga, Eliana Stabile, Florencia Bonsegundo and Mariana Larroquette are all one booking away from a one-match suspension.
Goalkeeper Vanina Correa will wear the captain's armband, and she will be shielded by the central defensive pairing of Mayorga and Aldana Cometti, who will be looking to help their country keep just their second clean sheet at a World Cup finals.
As for their opponents, Magaia was forced off after picking up an injury while bundling home the opening goal against Sweden, but the 28-year-old should be fit to take her place in the starting lineup.
If Magaia is available for Thursday's contest, South Africa Desiree Ellis could be tempted to name an unchanged side.
Refiloe Jane and Kholosa Biyana are both one yellow card away from being suspended after being cautioned in the defeat to Sweden.
Argentina Women possible starting lineup:
Correa; Braun, Mayorga, Cometti, Stabile; Nunez, Falfan, Benitez, Banini, Bonsegundo; Larroquette
South Africa Women possible starting lineup:
Swart; Ramalepe, Mbane, Gamede, Holweni; Jane, Biyana; Seoposenwe, Motlhalo, Magala; Kgatlana