West Indies, who bowled England out with more than five overs to spare, had set themselves up with a good chance of victory when they amassed 289 for five in their 50 overs, having won the toss and elected to bat first.
Powell had opener Alastair Cook caught by Dwayne Smith at backward point for 18 and talismanic but off-form batsman Kevin Pietersen, out for a duck, caught by Devon Smith in the slips. He also had Matt Prior caught by keeper Denesh Ramdin for one.
When Ian Bell, batting at number three, was out for 27, caught by Dwayne Smith off Fidel Edwards, Owais Shah and captain Paul Collingwood dug in to try and stop the rot.
However, Dwayne Smith had Shah caught by Ramdin for England's top score of 51 and Collingwood was bowled by Dwayne Bravo for 44, leaving Edwards to help wipe up the tail for a tally of three for 30.
For West Indies, Runako Morton, who was unbeaten, and opener Chris Gayle, who hit eight boundaries, both made 82 while Bravo chipped in with a quick-fire 42 off 24 balls.
England thought they had seriously dented the West Indies challenge when in-form Shivnarine Chanderpaul, declared fit after being doubtful with an ankle injury and batting at number three, was out for 33.
They had not counted, however, on Morton and Bravo's fifth-wicket stand of 92 off 54 balls after poor fielding had handed Gayle and Morton second lives.
Chanderpaul, whose unbeaten century in the second match at Edgbaston in Leeds helped West Indies square the series 1-1 and helped earn him Saturday's vote as man-of-the-series, was caught by Pietersen off Liam Plunkett.
Plunkett, whose first wicket was that of captain Gayle, caught and bowled, also dismissed Marlon Samuels for nine, caught behind by wicketkeeper Prior, for a haul of three for 59, while James Anderson took two for 51.