Paul Stirling and Andrew Balbirnie both hit centuries in the shock victory.
David Willey added a rapid half-century at the end of the innings.
The opener scored 82 off 41 balls in a four-wicket win at Southampton.
The 34-year-old took his 500th Test wicket earlier this week.
The opener against Ireland on Thursday is England’s first on these shores since being crowned world champions.
England have plumped for the more tried and trusted fringe players such as James Vince and Sam Billings.
England host Ireland on Thursday, Saturday and Tuesday at the Ageas Bowl.
Morgan’s side beat New Zealand in dramatic fashion at the home of cricket.
The tournament is scheduled to start on October 18 until November 15 in Australia.