Argentina's victory, their fourth in five outings, gives them 12 points and ousts Olympic champions Germany from the semifinal race.
Germany, who later today play South Korea in their last match, have six points from four matches after suffering identical 01 defeats against Argentina and hosts The Netherlands.
Olympic silver medalists The Netherlands were the first to secure passage into the semifinals from Group B with four straight wins.
This is only the second time in World Cup history that the Germans have not advanced to the semifinals. The only previous occasion was in the inaugural World Cup in 1971 when Kenya made the semifinals at the expense of West Germany.
South Africa's lone goal came from the sticks of Clinton Panther, but Argentina had by then done enough to secure entry into the semifinals.
Argentina's previous best finish in the men's World Cup was sixth position they secured in the 1986 and 2002 World Cups.