Chasing a Duckworth-Lewis-Stern (DLS) reduced score of 188 in 34 overs at a rain-lashed Kensington Oval in Bridgetown, West Indies appeared to have got off to the perfect start as Carty (50) combined with Alick Athanaze (45) for a 76-run partnership, but spinner Will Jacks tore through their middle order.
Jacks (3-22) picked up three key wickets as West Indies slumped from 1-78 to 6-135.
With his side reeling, Romario Shepherd hit a crucial 41 to push them over the finish line with 14 balls to spare, though the allrounder benefited from a massive slice of luck when he was dropped on 18 by Liam Livingstone on the boundary rope.
West Indies won the series 2-1.
Earlier on Saturday, Forde (3-29) took the wickets of Phil Salt (four), Will Jacks (17) and Zak Crawley (zero) to leave England on 3-45 in an excellent spell on his ODI debut.
"Getting a victory is a dream come true on my debut," Forde said.
"It was special for me. I am 21 and I am living my dream. I thank all the guys for making it possible. They have welcomed me with open arms and it has been an easy camp so far."
The tourists' innings was rescued by Ben Duckett, who plundered 71 off 73 balls, while Liam Livingstone was able to shrug off his recent struggles with the bat to contribute 45 runs as the visitors posted a total of 206 in a rain-reduced 40 overs.
Shepherd removed Duckett and Livingstone in back-to-back overs to stymie England's progress, with the visitors posting a total of 206 in 40 overs at the Kensington Oval in Barbados.
The series victory, West Indies' first over England since 2007, will give the hosts a massive boost after they failed to qualify for the recent 50-over World Cup.
For England, however, it will raise even more questions about the future of their ODI team, coming off the back of a disappointing World Cup exit.
"This is the start of a long journey for this side," England skipper Jos Buttler said.
"There are some young guys who have got their first taste of ODI cricket and have hopefully learned lot and can go on and we can build something for the future."
The two sides will now face each other in a five-match Twenty20 series, with the first game to be played at the same venue on Tuesday.
