Resuming the third day at 308/4, the hosts lost five wickets in quick succession before Ravichandran Ashwin (35) and Shardul Thakur (4 not out) added 28 runs for the last wicket.
Ajinkya Rahane (80) fell early in the morning session after adding just five runs to his overnight score.
Kuldeep Yadav too, fell cheaply on a Holder delivery after contributing with six runs while Umesh Yadav (2) also failed to score as India's scorecard read 339/9.
Ashwin and Shardul then showed some resistance to take their side past the 350-run mark.
Gabriel finally performed the last rites as he bowled out Ashwin as India managed to take a 56-run lead in reply to West Indies first innings total of 311 runs.
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