It was also Ireland's highest total in their 152 years of competition, beating 462 set way back in 1863.
In another record, Morgan, who eclipsed Ivan Anderson's 198 in 1973, shared an Intercontinenal Cup and Irish record partnership of 360 with Andre Botha.
In reply, the UAE were struggling on 194-6 after 63 overs.
The home side put on 75 for the first wicket but Derbyshire paceman Boyd Rankin claimed Shadeep Silva's wicket, with Andrew White taking the catch.
The wickets continued to tumble with White, Kyle McCallan, Andre Botha (two) all claiming wickets and vice-skipper McCallan also crucially running out Arshad Ali who had struck an impressive 75.
Earlier, Botha had played his part in the mammoth Irish partnership which was finally broken when he mis-timed a drive and was caught at mid-off for 157 from 216 balls, his highest score for Ireland.
Morgan continued in accomplished fashion, with 24 fours and a six in his epic 238-ball innings, before Trent Johnston declared nine overs before lunch.