Chasing 150 to win, India lost wickets at regular intervals and the required run rate climbed beyond their reach as Debutant Tilak Varma top-scored with 39 off 22 balls.
The visitors needed 11 off the final over but Shepherd kept a cool head to concede five runs and picked up two wickets to condemn India to defeat in their 200th T20 international. Only Pakistan having played more matches in the shortest format of the game at 223.
India were without experienced players including Rohit Sharma and Virat Kohli who were left out of the squad.
"We were right in the chase. We made some errors which cost us, but it is fine," India captain Hardik Pandya said.
"A young team will make mistakes. Throughout the game, we were in control. I have always believed that in T20 cricket, if you lose wickets, it becomes difficult to chase down a total."
West Indies won the toss and opted to bat but struggled to get going as Yuzvendra Chahal removed both openers.
Rovman Powell (48) shared 38-run partnerships with Nicholas Pooran (41) and Shimron Hetmyer (10) to lift the hosts to 149. Arshdeep Singh pitched in with two wickets for the visitors, dismissing Powell and Hetmyer.
The second game of the five-match series will be played in Guyana on Sunday.
