Bains cracked 14 fours and seven sixes to notch up a whirlwind 134 in just 89 deliveries and along with his opener partner Akhil Herwadkar (88) forged a match-winning 218 partnership to take India home in just 28 overs.
Today's win was India's fourth on the trot and the home side made it to the final without losing a match and two games left to play. South Africa Under-19 side are on 12 points, four less than that of India Under-19.
Abhimanyu Lamba (2 for 55) took two wickets, while Kuldeep Yadav, Deepak Hooda and Ricky Bhui scalped one each.
Chasing 246 to win, Bains and Herwadkar scored runs at will as it started raining fours and sixes at Port Trust Diamond Jubilee Stadium here.
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Bains was the more dominating between the two as he showed little respect for the visiting bowlers, plundering them all over the park as India always kept more than eight runs per over.
Earlier, debutant C Chitumba was the highest scorer for Zimbabwe Under-19 side as he hit 13 fours in his 80-ball innings of 83. Wicket keeper Joylord Gumbie was the other notable contributor with 60 runs. He had 10 fours in his 104-ball stay.