Jos Buttler's career-best 67 saw the tourists' to a total of 152 for seven batting first with left-arm seamer Krishmar Santokie justifying his inclusion in place of injured spinner Sunil Narine by claiming four for 21 to earn the "Man of the Match" award yesterday.
Cruising at 111 for two in the 15th over, the hosts lost three wickets for five runs before captain Darren Sammy belted an unbeaten 30 off just nine deliveries to take his team to 155 for five with seven balls to spare.
"This is all about building towards the T20 World Cup," said a delighted Sammy.
"It's good that all the guys are firing and when you sit down and plan, then execute on the field, it feels good."
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Handicapped by the absence of regular captain and key bowler Stuart Broad because of injury, England nevertheless proved far more competitive than in the first match on Sunday, although their poor start with the bat and inability to sustain the effort in the field eventually cost them dearly.
"We showed a lot of fight though, which is good heading into the World Cup."
They were labouring at 26 for three in the fifth over after Morgan chose to bat first before Buttler joined opening batsman Alex Hales in putting on 76 for the fourth wicket.
The wicketkeeper-batsman needed more than a bit of luck but was particularly impressive, hammering five fours and three sixes off 43 balls to put his team in position to post a competitive total.