The Indian women put up a valiant fight and created numerous scoring chances in the second half, only to be denied by a resolute South African defence, to finish in the third position in Group A.
Toppers New Zealand and South Africa have qualified for the semifinals from Group A.
South Africa scored through Tarryn Bright (14th minute), Dirkie Chamberlain (35th) and Illse Davids (54th), while Jaspreet Kaur (34th) and Rani Rampal (59th) were the goal getters for India.
The Indian girls showed glimpses of their skill but failed to convert their build-ups into meaningful chances.
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Both India and South Africa earned as many as six penalty corners in the match but could utilise just one each.
South Africa took the lead in the 14th minute when Bright scored from a variation from their first penalty corner.
India earned as many as three penalty corners in the opening half thereafter but failed to convert a single one.
India's joy was shortlived as they conceded a soft goal in the next minute when an unmarked Chamberlain scored from close range as New Zealand went into the breather with a 2-1 lead. After the change of ends, South Africa earned two penalty corners in quick succession, but wasted both.
But Davids scored from a rebound in the 54th minute after Dammons' initial shot was saved by Indian goalie Savita to increase South Africa's lead.
Needing two more goals in 15 odd minutes, India stepped up the pressure on the South African goal, but the Proteas backline stood tall to seal their place in the last-four stage.