Extending an excellent run of form from the previous ODI series in India in January, the England captain accelerated from a painstaking start, his innings of 107 was timed to perfection in lifting his team to a competitive total after they were put in to bat on a rain-interrupted morning.
He faced 116 deliveries and struck 11 fours and two sixes after coming to the crease with his side in early trouble after fast bowler Shannon Gabriel removed opening batsman Jason Roy and new Test skipper Joe Root in successive overs.
That dismissal brought in Ben Stokes and the aggressive all-rounder did not disappoint, belting 55 off 61 deliveries with three sixes and seizing the initiative from the West Indies with a 110-run fifth-wicket partnership, ended by a catch at long-on off leg-spinner Devendra Bishoo.
Morgan reached three figures in fine style, hoisting Carlos Brathwaite for a huge six over midwicket in the 48th over before the bowler had the last laugh, running out the left-hander in the final over of the innings.
Exciting all-rounder Rovman Powell was surprisingly omitted from the West Indies final eleven with Jason Mohammed returning to the middle-order.
Like the home team, England have gone the way of a twin-spin option with Ali and Adil Rashid seeking to exploit a dry surface in defence of that formidable total.