Morgan did so in his 163rd match as captain, while Dhoni led India in 332 matches.
Morgan bettered Dhoni when he struck first of his four sixes on his way to a brilliant 106 off 84 balls against Ireland in Southampton in the third and final ODI of the series.
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The remarkable thing is that he reached there in his 163rd game as captain, while Dhoni led India in 332 matches.
Ricky Ponting (171 in 324 matches), Brendon McCullum (170 in 121) and AB de Villiers (135 in 124) also feature among the top five.
Despite Morgan's hundred, however, England lost by seven wickets, as Ireland handsomely chased down the hosts' intimidating target of 329.
Experienced opener Paul Stirling (142) and skipper Andy Balbirnie (113) made outstanding hundreds to help their country not only pull off its most amazing win in recent times but also gain crucial 10 points towards the ICC ODI Super League.
The hosts, though, won the series 2-1.
(Inputs from Sportstar)