The Indian batsmen scored an intimidating 339 for six after opting to bat at Sabina Park. The hosts responded with 319 in 48.1 overs.
For the West Indians, Shivnarain Chanderpaul top scored with 63, while wicketkeeper Denesh Ramdin played a sparkling 29-run knock.
Earlier, Yuvraj treated the West Indian bowlers with utter disdain, clobbering them for seven huge sixes and 10 boundaries apart from sharing a crucial 135-run stand with Dinesh Karthik (67).
Skipper Mahendra Singh Dhoni (41), Yusuf Pathan (40 unbeaten) and Harbhajan Singh (21 not out) also chipped in with useful contributions.
With the wicket of Chanderpaul in the 36th over it looked all over for the hosts but their lower order batted with steely resolve and made it an edge-of-the-seat contest.
West Indies required 21 off the last two overs with one wicket in hand but Ashish Nehra removed Ramdin in the first ball of the 49th over to bring a huge relief for his side.
Ramnaresh Sarwan (45) and Runako Morton (42) did well and got the starts for the West Indies but could not convert those into big knocks.
Jerome Taylor (21) and David Bernard (19), batting at number seven and nine respectively did their best but their effort went in vain in the end.
For India, Nehra (3/49) and Yusuf Pathan (3/56) took three wickets each. It was raining sixes as 23 of them were hit in the match. (ANI)