The 21-year-old left-hander struck an unbeaten 91 from 106 deliveries as Essex coasted to an eight wicket C&G Trophy win with six of their 43 overs to spare.
Cook did experience a few anxious moments early on as both John Mooney and Trent Johnston passed the outside of his bat, but once he settled in, the Irish were left fighting a losing battle.
He repeatedly penetrated the field with fluent drives as he completed his half-century with his eighth four – a stroke which also brought up the 100 in the 21st over.
Even Saqlain Mushtaq and Shahid Afridi were unable to make an impression as Cook finished nine runs short of what would have been his first one-day century.
Grant Flower lent Cook great support following the dismissal of skipper Ronnie Irani, who was bowled by Mooney without a run on the board.
He scored freely enough to make 61 from 92 deliveries with the help of six fours and one six. His partnership with Cook was worth 163 in 30 overs.
Earlier, Ireland found themselves firmly on the back foot by the end of the sixth over of the innings, although they eventually reached 192.
In a shaky start, Ireland lost three wickets as Tony Palladino, twice, and Andre Adams made their presence felt.
Both got the ball to swing and seam quite considerably to leave the visitors 20 for three.
The poor start left Eoin Morgan and Botha to adopt a cautious approach in their attempt to repair the innings.
The duo succeeded to the extent that they added 79, although it took them 22 overs to gather those runs before Morgan became the first of Ryan ten Doeschate’s four victims.
Ireland had hoped Afridi would give them momentum.
He started by pulling off-spinner James Middlebrook for six from the first ball he received but he holed out to square leg from his fourth delivery to provide ten Doeschate with another success.
It was left to Botha, with the help of a few lusty blows from the tail, to give the Irish total an air of respectability.
Botha made 64 from 100 deliveries, five of which he dispatched to the boundary, and it was while seeking a sixth that he was bowled by Middlebrook.