Paul Stirling and Andy Balbirnie set up famous chase as Ireland hunt down 329 in the final over.
David Willey, Sam Billings lead hosts to series win after securing 4-wicket victory in second ODI.
David Willey sets up England victory as Sam Billings brings it home
England have confirmed they will host Pakistan in a three-Test series starting on 5 August.
Before home series Bangladesh will travel to Ireland on May 8 to play three ODIs and four T20Is.
A stunning last over blitz from Rashid Khan tied the game, before Joshua Little bowled a top Super Over conceding only 8 runs