South Africa A now trail India A by 14 runs with five second innings wickets in hand.
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Chasing an improbable 373-run target, West Indies finished at 314/6 when stumps were drawn on the final day.
Needing 97 to win, India A lost four wickets but eventually crossed the line and acquired a 1-0 lead.
West Indies A were bowled out for 180 in their second innings at North Sound.
India A were 70/1 after Shahbaz Nadeem picked up 5/62 to bowl out West Indies A for 228.
Left-arm spinner Nadeem then swung into action to further tilt it in India's favour as he cleaned up the middle order.
CSK, who have lost two consecutive matches for the first time since re-joining the tournament in 2018 and have been displaced from the first position in the points table too.
Sanju Samson’s hundred and Ajinkya Rahane’s 70-run knock went in vain as David Warner and Jonny Bairstow blitz powered Hyderabad to a five-wicket win against Rajasthan.
Sanju Samson scored an unbeaten ton while Ajinkya Rahane scored 70 to power Rajasthan to 198 against Hyderabad.