For the second match in a row England were unable to prevent West Indies scoring more than 100 runs in the last 10 overs, the tourists taking 116 off an inexperienced and wayward seam attack this time.
Morton, dropped on four, shared a fourth-wicket stand of 85 with captain Chris Gayle (82), dropped on four and 20, and then put on 92 with Dwayne Bravo (42). He faced just 89 balls with one six and six fours.
Stuart Broad was the most expensive England bowler, his nine overs costing 71 runs
Curiously, neither recalled spinner Monty Panesar (six overs for 28) or Dimitri Mascarenahs (eight overs for 28) bowled their full, 10-over allocation.
Liam Plunkett (three for 59) and James Anderson (two for 51) shared the wickets between them.
West Indies total was made without a major contribution from left-hander Shivnarine Chanderpaul.
A thorn in England's side, having averaged over 148 and batted for more than 24 hours during the hosts' 3-0 Test series win, Chanderpaul made 116 not out in West Indies 61-run victory in the second one-day international at Edgbaston where he sustained an ankle injury.
Chanderpaul was out for 33, his first dismissal this series, when he slogged Plunkett and Kevin Pietersen, running back some 20 yards from mid-wicket, took a well-judged catch.
Marlon Samuels, who'd made 77 during a stand of 175 with Chanderpaul at Edgbaston, then exited for nine when, trying to run Plunkett to third man, he flat-footedly guided the ball to wicket-keeper Matt Prior and West Indies were 108 for three.
Prior, though, missed a tougher chance when, standing up, he dropped Morton, on four, off a thin outside edge against medium-pacer Mascarenhas.
By then Gayle had completed an unusually patient 85-ball fifty.
But in sight of a hundred he popped a return catch to Plunkett.
Bravo though maintained the momentum with a dashing 24 ball-innings.
Morton went to fifty by pulling Broad for four. He followed that up in the same over by driving Broad, off the backfoot, for a superb straight six.