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Asked to bat, Raut continued her rich vein of form with an unbeaten 104 while Harmanpreet smashed a blazing half-century to power India to a 266 for four in 50 overs.
In reply, opener Lizelle Lee (69), skipper Laura Wolvaardt (53), Mignon du Preez (61), and Lara Goodall (59 not out) smashed half-centuries to guide South Africa home.
The tourists scored 269 for three in 48.4 overs to take an unassailable 3-1 lead in the five-match.
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The two sides will play the fifth and final ODI here on Wednesday.
Brief Scores:
India women: 266 for 4 in 50 overs (Punam Raut 104 not out, Harmanpreet Kaur 54; Tumi Sekhukhune 2/63)
South Africa women: 269 for 3 in 48.4 overs (Lizelle Lee 69, Mignon du Preez 61, Lara Goodall 59; Mansi Joshi (1/43), Rajeshwari Gayakwad (1/39), Harmanpreet Kaur 1/38 )