After a steady start, Morgan went through to his 10th ODI ton as England accelerated late in the innings to post 296-6 from their 50 overs, Sam Billings (52) and Ben Stokes (55) also making half-centuries.
Fifties from Jason Mohammed (72) and Jonathan Carter (52) gave the hosts hope in reply but, ultimately, they came up short, Chris Woakes (4-47) and Liam Plunkett (4-40) each taking four wickets as the West Indies were bowled out for 251.
