He was India captain Rohit Sharma's opening partner in the home T20 series against Afghanistan earlier this year but his place looked under threat as he struggled for runs in the IPL
Shot out for 181 in their first innings and made to follow on, West Indies collapsed for 196 in their second in third day's final session with Kieran Powell topscoring for them with a counter-attacking 83.
Left-arm spinner Kuldeep Yadav (5-57) was the pick of the Indian bowlers, claiming his first five-for in test cricket as West Indies lost 14 wickets on Saturday.
Hyderabad hosts the second and final test from Friday.