World Twenty20 champions England, set 173 to win, finished on 173 for three with Alex Hales making an England best 99 at this level.
Together with Ravi Bopara (59), Hales put on 159 for the second wicket — the third highest partnership for any wicket in all Twenty20 internationals.
Opener Hales, on his Nottinghamshire home ground, faced just 68 balls with four sixes and six fours.
But, in sight of becoming just the seventh player to make a Twenty20 international hundred, he was yorked by Fidel Edwards.
Earlier the West Indies, who slumped to 57 for three at the halfway stage, recovered to 172 for four on the back of Dwayne Smith’s 70 and Dwayne Bravo’s 54 not out.