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 [ Images ] (52).
Needing 15 off the last over, senior team reject Suleiman Benn (17 no) clobbered Bhuvenshwar Kumar for two huge sixes as the home team chased down the target with two balls to spare.
India's middle-order collapsed yet again. They were 106/3 after 14 overs but lost the next seven wickets for an addition of 24 runs in four overs.
Left-arm spinner Benn (3/24) was 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 [ Images ] (11) was holed out at mid-on off left-arm seamer Krishwar Santokie's bowling.
Rohit and Shikhar Dhawan [ Images ] then 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 by seamer Jason Holder while trying to scoop one over the 'keeper's head. Cheteshwar Pujara [ Images ] (8) wasn't comfortable and 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 to dismiss the Mumbai [ Images ] batsman.
Rohit cut one straight into the hands of Santokie at point to find his way back to the pavillion.
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 to restrict the West Indies to 78 for five in 13 overs. The Windies then needed 53 runs from the last five overs. Jonathan Carter (35) got some useful runs but it was left to Benn, whose big hits changed the course of the match.
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 n.o.)
West Indies A win by 3 wickets.