Chasing a target of 288 runs set by India on a slow surface West Indies chased the target in 47.5 overs. West Indies made 291 for the loss of two wickets.
The duo shared a decisive 218-run stand for the second wicket after the fall of Sunil Ambris in the fifth over.
Earlier, India had recovered to 287 for eight after being put in to bat with Shreyas Iyer (70 off 88) scoring his third consecutive half-century and Rishabh Pant (71 off 69) returning to form to silence his critics.
The second game of the three-match series will be played in Visakhapatnam on Wednesday.