NUIG were too good at Clanna Gael, Fontenoy, and had the hard work done by half-time, having established a 3-10 to 0-3 interval advantage.
It was one-way traffic more or less from the start as NUIG, with rising Mayo star Conor O’Shea at midfield, dictated the terms of engagement.
Their fluent interplay was too much for Trinity to handle and the scores flowed freely for the winners.
NUIG were 0-5 to 0-2 clear before Galway’s Michael Daly notched the game’s opening goal midway through the first half.
A Tadhg McGahern error let in Antrim’s Owen Gallagher for NUIG’s second goal, before leading scorer Kevin Finn added a third approaching half-time.
Trinity managed just a single point from play in the first half, converted just before the interval by one of their better players, David Boothman.
Both teams ran their respective benches in a second half as the game petered out to an inevitable conclusion.
Boothman kicked the opening score of the second half from a free but normal service was resumed when Finn responded with a point for NUIG.
Kevin McDonnell, NUIG’s outstanding corner back from Sligo, even had the time to bomb forward for a point as the winners continued to turn the screw, before points followed from Mayo’s Adam Gallagher and another impressive performer, midfielder Peter Cooke.
Trinity may have been outclassed from start to finish but coached by Down’s Conor Laverty, they were game right to the end.
And their undoubted industry was rewarded with the game’s final score when Michael O’Grady fisted the ball to the NUIG net from a booming long-range delivery.
This was routine stuff for NUIG but the stakes and the ante get much higher next time out when they tackle UCD for a place in the quarter-finals.
K Finn 1-3 (0-1f), M Daly 1-2, O Gallagher 1-0, A Gallagher (1f) & P Cooke (3f) 0-3 each, K McDonnell, J McManus & S Moran 0-1 each.
M O’Grady 1-0, D Boothman 0-3 (2f), M O’Sullivan 0-1f.
D O’Sullivan; K McDonnell, D Cunnane, L Burke; J McManus, D Murray, A Nolan; C O’Shea, P Cooke; S Moran, M Daly, A Gallagher; K Finn, O Gallagher, C Davey.
P Mannion for Finn (43), E Tierney for O Gallagher (43), S Conroy for Davey (46), L Cullen for Cunnane (48), E Boland for Murray (52).
M Shiels; B Flynn, T McGahern, G Deery; C O’Donoghue, M O’Grady, K Archbold; S Cunningham, M Walsh; E O’Neill, E Keogh, D Boothman; R McCullagh, C O’Driscoll, M O’Sullivan.
S Ward for McGahern (37), S Mulhern for Walsh (38), L Tynan for McCullagh (41), R O’Hanlon for Shiels (46), J Bell for Flynn (46), C MacGearailt for O’Sullivan (48).
C Reilly (Meath).