Du Plessis made 120 in a South African total of 269 for eight after they won the toss and batted on a slow pitch.
Indian wrist spinners Yuzvendra Chahal and Kuldeep Yadav took five wickets between them and the South Africans struggled to achieve momentum as they slumped to 134 for five in 27.5 overs.
Du Plessis, though, batted confidently and shared stands of 74 with Chris Morris (37) and 56 with Andile Phehlukwayo (27 not out) to get his team to a competitive total.
Leg-spinner Chahal took two for 45 and left-arm wrist spinner Yadav took three for 45 and kept tight control during the middle overs.
There was a scare for India early in the innings when captain Virat Kohli jarred his left knee when attempting a sliding stop on a soft outfield.
Kohli left the field twice to receive treatment but appeared to be moving freely when he took a diving catch to dismiss David Miller and made a smart pick-up and throw in attempting a run-out.
Du Plessis reached his ninth one-day international century off 101 balls with 11 fours and added two sixes before being caught at long-off in the last over after a 112-ball innings.
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