England batted first with a fine 74 from opener Phil Salt helping the tourists recover from 4-24 to post a respectable 8-263 - a late flurry  from the bat of fast bowler Jofra Archer (38 not out) helping their cause.
Archer struggled with the ball, however, as Keacy (128 not out) posted his first international ton and King (102) made his third ODI century in a second-wicket partnership of 209 to guide the hosts to victory.
England take on the West Indies again in the first of five Twenty20 Internationals at Barbados' Kensington Oval on Saturday, with white-ball captain Jos Buttler in line for a potential return from injury.
Liam Livingstone had notched a maiden ODI century to help England square the series 1-1 on Saturday, but the stand-in skipper's wicket was one of four to fall inside the first 10 overs at Kensington Oval, with only 24 runs on the board.
Salt's 70-run stand with allrounder Sam Curran helped England recover, while Dan Mousley's maiden ODI half-century dragged the tourists back into the contest.
A mid-spell injury to the hosts' Romario Shepherd provided England with a further boost, with Sherfane Rutherford forced to come into the bowling attack.
England plundered 57 runs off Rutherford's 3.5 overs, with Archer's big-hitting 38 from 17 balls, including three sixes, doing the damage.
"We battled back really well (with the bat)," Livingstone told TNT Sports. "The boys in the middle put on a decent partnership and ended really well. Ultimately we didn't get enough runs.
"Disappointed with the end to the series but there have been a lot of good parts."
West Indies captain Shai Hope said his side's dominance had pleased him most.
"We asked for consistency and discipline, and that's exactly what the guys did. The main thing if you want to be an elite team is that you've got to do things consistently," he added.
"It's a big plus for us, the work is really showing. The guys are putting a lot of work in off the field. It's a great confidence booster, especially for the batting unit and going forwards I'm sure we'll have a lot more runs to come."
England struck early when Jamie Overton removed opener Evin Lewis for 19 but the partnership between King and Carty ended the tourists' hopes. It was only the third time a West Indies ODI partnership accumulated more than 200 on home soil.
King was clean bowled by Reece Topley as the hosts closed in on victory, with Carty, who finished the series as the highest run scorer, hammering one final boundary to seal the win.
It was England's third successive ODI series defeat since their disappointing World Cup in India last year.
