England finished with 274-4 having been set a target of 269 by the Irish, with captain William Porterfield scoring 112 for Ireland.
After some worrying moments for England as the top of their order failed to fire, Bopara and Morgan put on an unbeaten 226-run partnership. Scoring at a rate of eight an over, the two steadied the English attack, which only managed to produce one other score over 10.
Morgan's 124 off 106 balls included four huge sixes, while Bopara smashed five out of the ground in his 101 off 75 balls. Tim Murtagh was the only Irish bowler to find success, taking 3-33.
The English innings started shakily, leading them to a worrying 25-3 after the end of the ninth over. When Taylor's wickets were rattled by Murtagh, England were 48-4, and 3.1 runs behind the required run rate.
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But Bopara and Morgan immediately went about exposing the Irish bowling. Morgan, who is of Irish descent, delivered an inspiring captain's knock to secure victory.
By then, he'd hit 14 of the 142 balls he faced to the boundary, and one six. The rest of the batting lineup failed to capitalize, with the extras tally of 32 the second-highest total on the scorecard.