The match which was reduced to 18-overs per side after a rain delay saw India A post a modest 130 courtesy half century by Rohit Sharma (52).
Needing 15 off the last over, senior team reject Suleiman Benn (17 no) clobbered Bhuvenshwar Kumar for couple of huge sixes as the home team chased down the target with two balls to spare.
The middle-order collapsed yet again as India who were 106/3 after 14 overs, lost next seven wickets for addition of another 24 runs in four overs.
Left-arm spinner Benn (3/24) was certainly the man, who made the difference in the end.
India 'A' opted to bat after winning the toss but India's opening blues continued as Ajinkya Rahane (11) was holed out at mid-on off left-arm seamer Krishwar Santokie's bowling.
Rohit and Shikhar Dhawan took India past 50 in the eighth over with the former playing some lovely shots.
Having added 49 runs for the second wicket, Dhawan (21) who was playing second fiddle to Rohit was bowled off seamer Jason Holder's bowling trying to scoop one over 'keeper's head. Longer format specialist Cheteshwar Pujara (8) wasn't comfortable as he was bowled round the legs by Samuel Badree.
Rohit reached his half-century in the 14th over but it was left-arm spinner Benn who came back for his second spell dismissed the Mumbai batsman. Rohit cut one straight into the hands of Santokie at point.
The slide started from there on as Wriddhiman Saha (1), Jalaj Saxena (0) and Manoj Tiwary (4) were out in quick succession ending chances of a fighting score.
Indian bowlers did well as they had restricted West Indies to 78 for five in 13 overs as they needed 53 runs from the last five overs. Jonathan Carter (35) got some useful runs but it left to Benn whose big hits changed the course of the match.
Brief Scores (18 overs/side): India A 130 all out in 18 overs (Rohit Sharma 52, S Dhawan 21, S Benn 3/24)
West Indies A 131/7 in 17.4 overs (J Carter 35, S Benn 17 no). West Indies A win by 3 wickets.