Morgan was booed as he came to the crease on his home ground at Malahide but departed to a standing ovation as his and Ravi Bopara’s world record fifth-wicket partnership of 226 swept the visitors to victory.
A youthful, experimental England side had looked in trouble when they slipped to 48-4 in reply to Ireland’s 269-7, which was fuelled by home skipper William Porterfield’s 112.
“It was very satisfying, particularly getting over the line,” said Morgan. “I have won a trophy here with this club and it was a fantastic feeling.
“Centuries at No5 are few and far between. Not many people do it. You have to be happy seeing the innings out and contributing at a reasonable rate. Then Ravi has got a hundred coming in behind me at six. That is one hell of an achievement.”
Paceman Boyd Rankin, another ex-Ireland player, was the pick of England’s bowlers with 4-46 and one of three England debutants, along with Michael Carberry and Gary Ballance.
England face Australia, who crushed Scotland by 200 runs yesterday, in the first of five ODIs on Friday at Headingley.