Both were batting on 69 (176 balls with 11 fours) and 36 (64 balls with four boundaries) respectively after captain Kirk Edwards (18) and Narsingh Deonaraine (12) were the two batsmen to be dismissed during the session.
Brathwaite, who had been a thorn in the flesh for Indian bowlers in the Mysore Test, played his usual game of sticking to the wicket as his favourite player Shivnaraine Chanderpaul would have done. The Barbadian reached his second fifty of the series in 197 minutes from 138 balls.
The left-handed Guyanese batsman was first dropped on 12 by V A Jagadeesh off Mohammad Shami and then by Mohammad Kaif off Abhishek Nayar on 27.
After reaching 67 for one at lunch, the visitors lost their second wicket in the first over after the break.
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Left-arm orthodox spinner Bharghav Bhatt, who gave a breakthrough just before lunch, struck big time by removing in-form West Indies Captain Kirk Edwards, who was stumped by Uday Kaul for 18.
The 34-year-old, who has taken 295 international wickets from 88 Tests and 282 wickets from 200 ODIs, has been left out of the India squad since last year after he picked just one wicket against England at the Eden Gardens.
Earlier, West Indies lost one wicket before lunch in their bid to give a solid platform for the later batsmen to capitalise on and put a big total as they did in the Mysore Test.