The pair bettered the previous record opening partnership of 304 set by the Pakistan duo of Imam-ul-Haq and Fakhar Zaman against Zimbabwe in 2018.
The duo fell five short of the record partnership across any wicket. That also belongs to the Windies as Chris Gayle and Marlon Samuels had put on 372 against Zimbabwe for the second wicket in the 2015 World Cup at Canberra.
It was also the first time that both the Windies openers had hit a century in the same game.
They were both dismissed in the 48th over, Campbell top-edging Barry McCarthy to mid-off with Hope falling three balls later when he holed out to deep square-leg.
McCarthy's figures of two for 76 in a maximum of 10 overs were almost respectable amid the torrent of runs.
Campbell faced 137 balls, including 15 fours and six sixes, with Hope's 152-ball knock featuring 22 fours and two sixes.
Ireland's attack had sparked an England top-order collapse at nearby Malahide on Friday but had no answer as the West Indies ran riot in the opening match of a triangular series also featuring Bangladesh.
Faced with a mammoth chase, Ireland promptly collapsed to 21 for three before Kevin O'Brien's 68 at least gave the West Indies bowlers something to think about. But the West Indies were always in control with off-spinner Ashley Nurse taking four for 51 in Ireland's 185 all out.