In pursuit of a challenging total of 258 for victory in their allocation of 50 overs, West Indies had reached 81 for two from 18.2 overs when the rain swept across the ground.
Though the ground-staff worked tirelessly to conduct mopping-up operations, too much damage had been done from the persistent showers, and the umpires abandoned any ideas of resuming about an hour before the scheduled close.
Left-handed opener Sewnarine Chattergoon had given West Indies early hope.
He scored 46 from 53 balls before he was caught behind in the ninth over, but the match was hanging in the balance, when the rain arrived.
The outcome left West Indies as victors after they won the opening ODI last Thursday at Queen's Park Oval by one wicket, and the rain-affected second ODI on Saturday at the same venue by seven wickets under the Duckworth-Lewis Method.
Earlier, hal