England, sent in to bat, amassed 328 all out in exactly 50 overs before restricting the hosts to 142 in 39.2 overs for their biggest ever win by runs over the Caribbean side.
Opener Hales (110 from 107 balls), who returned to the team in place of Sam Billings after recovering from a broken hand, and Root (101 from 108 balls) put on 192 for the second wicket on an uneven pitch, a record for England against West Indies.
That laid the platform for the visiting side's huge total, but they needed some power-hitting from Ben Stokes (34 from 20 balls) to ensure they made it past 300.
Seamer Alzarri Joseph, 20, playing in just his third ODI, was the pick of the home bowlers with 4-76, including the wickets of Hayles and Root plus Moeen Ali for a first ball duck.
Root was dropped off Joseph whe he had one as Evin Lewis failed to hold on to a chance at square leg that should have been taken and might have changed the complexion of the game.
England’s seamers exploited the conditions superbly and decimated the West Indies top order, reducing the hosts to 45 for six as Chris Woakes (3-16 in eight overs) started the collapse and Liam Plunkett (3-27 from eight) joined in later on.
Only Jonathan Carter (46) offered any sort of resistance as West Indies limped along simply trying to bat out overs.
When Carter was the ninth wicket to fall to Steven Finn (2-35 from 10), a late flurry from number 11 Joseph (22 not out) did add a glimmer of respectability to the home side’s score.
The series win is a confidence boost for England ahead of the Champions Trophy trounament they host in June. Ailing West Indies failed to qualify for the eight-team event.
142 in 39.2 overs (Carter 46, Woakes 3/16, Plunkett 3/27) lost to England
328 (Hales 110, Root 101, Joseph 4/76) by 186 runs