Chasing 226 to win, India were reduced to 92/6 at one stage but Rohit Sharma came up to India's rescue as he, along with Harbhajan Singh, added 88 for the seventh wicket. He then took India home with Praveen Kumar, who scored an unbeaten 25 from just 15 balls.
After Darren Sammy had taken two wickets - Shikhar Dhawan and Virat Kohli - in his first over and when Lendl Simmons had pulled off a superb catch to dismiss the dangerous Yusuf Pathan it looked as if the hosts might finally claim a win, but Rohit Sharma and Harbhajan Singh had some other plans.
Harbhajan Singh made a useful contribution as he scored 41 from 64 balls which included one four and a six before he was caught by the wicketkeeper Baugh as he mistimed the shot trying to clear the park and giving West Indies a glimmer of hope.
Nevertheless Praveen Kumar picked up where he left off, smashing 25 from 15 as he proved able company to the classy Sharma.
There were almost four overs to spare when Sharma hit the winning runs, but it would have been a far easier task had Russell not gathered his 92 runs in just 64 deliveries.
It was a tale of batting collapses and late recoveries with for both teams. When West Indies batted, they were tottering at 96 for 7 in the 30th over before recovering to reach 225 for 8 in their 50 overs, thanks Andre Russell's magnificent 64 -ball unbeaten 92 (8x4, 5x6).
West Indies lost six wickets at one stage for 31 runs while India also lost four wickets for 32 runs in the middle overs before making a good comeback.
Interestingly, a run-out at critical junctures in both innings had a huge role in the context of the batting collapse for the teams.
West Indies were 65 for 1 in the 15th over when Ramnaresh Sarwan was run-out and the mini collapse occurred. India was seemingly cruising at 60 for 2 in the 16th over when Badrinath rather foolishly ran himself out which triggered a collapse.
Badrinath drove to mid-off rather firmly and set off for a single and realized late that his partner Parthiv had not responded. He tried to trace back his steps but it was too late even a despairing dive wasn't of any use.
It affected the concentration of Parthiv (46) who cut at a widish delivery from Devendra Bishoo straight into the hands of Russell stationed at gully.
During India's bowling, leg-spinner Amit Mishra (3 for 28) had once again befuddled the hosts but the bowlers couldn't polish off the tail as it resulted in West Indies crossing 200 from being down in the dumps at 96 for seven.
Largely it was on account of an unexpected hurricane from fast bowler Andre Russell who clobbered the bowlers with utter disdain.
Russell shared two important stands of 78 and 47 runs for eighth and ninth wicket with wicketkeeper Carlton Baugh (36)
and Kemar Roach (7 not out) to lead the recovery as 47 runs came off the final three overs.
Earlier, it was Sarwan's dismissal shell-shocked the hosts and galvanized the tourists to the extent that the entire innings came off the wheels in the next few overs.
Mishra built on this breakthrough with three wickets off successive overs.
He first had Marlon Samuels (1) feel for a delivery outside his off stump to be out stumped and then sent down a googly which Danza Hyatt (1) mistook for a leg-break and was bowled off an inside edge.
Top-scorer Simmons (45) then went forward in defence, only to find the big-turning leg break take the edge to first slip.
It brought Kieron Pollard to the crease in the 25th over and demanded some responsible batting. Pollard scratched around for 16 deliveries to score 6 runs before he was caught behind off Harbhajan Singh's bowling.
Munaf Patel came back for his second spell with the wicket of skipper Sammy in the 30th over as he made him edge one behind the stumps. West Indies were certainly down and out at 96 for 7.
However Baugh and Russell made a meal out of India's fifth bowler Yusuf Pathan who was hit for two successive sixes in the 40th over by the latter over midwicket.
Munaf finally broke the stand in the 46th over when Baugh lifted one into the covers for Shikhar Dhawan to take a simple catch.