Only a brilliant reaction save by UCD keeper Mark McGinley prevented Monaghan taking the lead on 24 minutes when he pushed away a powerful header by Alan Byrne after a corner by Jordan Keegan on the left.
College eventually broke the deadlock on 53 minutes.
A clever midfield ball from Robbie Benson found the unmarked Danny Ledwith and his effort from 20 yards found the corner of the net.
Monaghan were level on 69 minutes when Keegan’s cross from the left was headed home by the alert Conor Murphy from close range.
Morrison had the Students in front again on 80 minutes when pulling down a cross from sub Mark Langtry and shooting past Bennion from the edge of the box.
The icing on the cake came on 88 minutes when Paul O’Conor shot home from close range to stretch the home side’s lead after Chris Mulhall had cleverly created the opening on the left.
Keegan did have a late consolation goal for Monaghan in the third minute of added time — but it was all too late for Roddy Collins’ new boys.
UCD: McGinley; Douglas (Leahy 78), Kavanagh, D O’Connor, Nangle (Langtry 78); P O’Conor, Benson, Ledwith; Morrison, Mulhall, Rusk (Clarke 60).
MONAGHAN: Bennion; R Collins (Isichei 85), A Collins, Byrne, McMahon (Marks 66); Keegan, Mayer, Bayly, G O’Connor; Murphy, Humphrey (Griffiths 60).
Ref: Anthony Buttimer (Cork).