At the end of day's play, the Kiwi batsmen have put on 152 runs for the loss of 1 wickets and trail by 166 runs.
Williamson (66) and Latham (56) have also put on a partnership of 117 runs
Earlier in the day, Recovering from a slump in the first day, the last pair of Ravindra Jadeja and Umesh Yadav added 41 runs to take India's score past the 300-run mark.
India were eventually bowled out for 318 runs, having started at their overnight score of 291 runs for the loss of nine wickets.
At lunch on day two, the visitors had put up 71 runs for the loss of a wicket.
Martin Guptill (21) was the lone casualty as he was struck in front of his wicket by a Umesh Yadav delivery.
Indian skipper Virat Kohli introduced spin as early as the third over.
Though the pitch looks conducive to turners, the Indian spinners are yet to taste success.
A chance arrived in form of Tom Latham, but after a referral, the third umpire ruled in favour of the Kiwi.
Replay showed that though KL Rahul, the short leg fielder took the catch after it rebounded off Latham's foot, the ball touched the visor of Rahul's helmet, rendering the appeal null.
Since then, the two batsmen have put up a solid display of skills and concentration to pile up the runs.
Under the revised conditions, play will start at 9:05 am tomorrow instead of the scheduled 9:30 am start.
The over limit has also been increased to 98 overs to compensate for the loss of overs due to rain.
(Writing by Sudipto Maity)
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