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The hosts need a draw in the final Test, also in Ahmedabad from March 4, to reach the WTC final against New Zealand.
Prithvi smashed an unbeaten 227 off just 152 balls to help Mumbai post a mammoth 457/4 against Puducherry.
TV umpire C Shamshuddin oversaw several close calls on a frantic 13-wicket day which ended with India gaining the upper hand.
The stadium, which has a capacity of 1.32 lakh, was inaugurated by President Ram Nath Kovind on Wednesday.
Rohit was batting on 57 at stumps with Ajinkya Rahane on one at the other end with India eyeing a handy first-innings lead.
President Ram Nath Kovind inaugurated the world's largest cricket arena at Ahmedabad ahead of the third India-England Test.
Chasing a daunting target of 352, Railways were bowled out for 344.
Coach Chris Silverwood apologised for the confusion surrounding his departure last week, saying selectors had decided beforehand Moeen would be granted leave before the final two Tests.
The refurbished Sardar Patel Stadium looks colossal under lights but the first Test match in many years would mean that even the home team wouldn't expect a lot of advantage.
This was Kerala's second victory on the trot in Elite Group C.
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