Singh´s powerful hitting helped India amass 339 for six, the second highest one-day international score at Sabina Park, but the determined hosts ran them close as they were bowled out for 319 in the 49th over.
Chris Gayle (37) and Runako Morton (42) put on 65 inside 10 overs for the opening stand before Ramnaresh Sarwan (45) and an aggressive Shivnarine Chanderpaul (63) kept West Indies up with the run-rate.
The home team needed 25 to win off the last three overs with two wickets remaining but Rudra Pratap Singh bowled Sulieman Benn for seven.
Wicketkeeper Denesh Ramdin, who had kept the flame burning with a smart 29 in 26 balls, was then caught by Harbhajan Singh off Ashish Nehra.
Before Friday´s game only Pakistan, against Zimbabwe in the 2007 World Cup, had managed to surpass 300 in an ODI at Sabina Park.
West Indies´s total was a second-innings record at the ground.
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