England won the toss and chose to field at Malahide. The visitors made two early breakthroughs, with Irish-born Boyd Rankin taking the wickets of Paul Sterling and Ed Joyce cheaply.
Niall O'Brien was next to go, falling to a James Tredwell delivery that went straight through and bowled him.
But it wasn't all bad news for Ireland. While wickets fell around him, Will Porterfield progressed to a brilliant century off 132 balls—reaching his ton with a six off the bowling of Rankin.
Rankin had him bowled soon after to take his haul to four wickets, but Porterfield's innings allowed the Irish to reach a respectable total of 269-7 from their 50 overs.
England's reply began badly, with Michael Carberry falling LBW early to Trent Johnston. Luke Wright played-on to the bowling of Tim Murtagh, and when Murtagh claimed Gary Ballance caught behind soon after England were reeling at 25-3.
James Taylor was next to go, another victim to Murtagh.
That brought Morgan and Bopara to the crease together. From there, England's fortunes changed dramatically.
Morgan reached 100 with a six, with Bopara making three figures to join him. No sooner had Bopara brought us his century, than Morgan smashed another six to ensure victory.
England's success will be seen as good preparation for Friday's meeting with Australia at Leeds.
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