On a tricky Barbados surface with tennis ball bounce and early movement, England stumbled to 24 for four after 9.5 overs before Phil Salt curbed his attacking instincts in a battling 74 from 108 balls.
Dan Mousley's 57 off 70 deliveries - his first international fifty - plus 40 from Sam Curran was followed by riotous late-innings cameos from Jamie Overton and Jofra Archer but a total of 263 for eight was overhauled by eight wickets and seven overs to spare by the Windies.
Overton claimed a wicket in his first over but England's seamers and spinners alike were largely nonthreatening as King and Carty capitalised on better batting conditions under floodlights.
King ended a run of 12 innings without an ODI fifty by amassing 102 off 117 balls while Carty's 128 not out off 114 deliveries was his maiden international hundred, lifting the Windies to a 2-1 series win.
England lost both white-ball series last year, as well as in Tests and T20s in 2022, while this was a 13th reverse in 20 ODIs for a side that have given youth and inexperience a chance on this visit.
After losing the toss, England's work was cut out for them at a ground where the chasing team have won seven of the past eight ODIs and they were in deep trouble early on a seamer-friendly pitch.
They did not help themselves as Will Jacks nicked off, while Alzarri Joseph took out his apparent frustrations at field placings with a 92mph bumper that brushed the glove of Jordan Cox, whose muted start to his England career continued.
Jacob Bethell was provided width but his cut was gobbled up by a terrific Roston Chase catch before Liam Livingstone, whose unbeaten 124 on Saturday squared the series in Antigua, edged a loose drive through to Shai Hope.
Having watched the carnage unfold at the other end, Salt led the rebuild, putting on 70 with Curran then Mousley, as the opener batted against type, steadily accumulating over outright attacking.
While he deposited Romario Shepherd over deep midwicket, Salt, dropped on 52, succumbed to his first proper show of intent, albeit following a superb relay catch as King plucked the ball out of the air before offloading just as he was about to tumble over the rope to the by-standing Joseph.
Mousley attacked the Windies spinners and then tucked round the corner for four after Romario Shepherd tripped in his delivery stride and fell over, which left Sherfane Rutherford having to pick up the slack.
After a quickfire 32 off 21 from Jamie Overton, Archer launched three leg-side sixes in his 38 not out off 17 - his highest score for England and bettering his previous ODI best of eight not out.
Rutherford conceded 44 in his final two overs, including 25 off the last, as Overton and Archer ushered England to a total in excess of 250, which would have seemed fanciful a few hours earlier.