The hosts dominated for most of the first-half with Darren Hughes, Dick Clerkin and Conor McManus impressing.
Despite hitting eight wides Monaghan led 1-9 to 1-2 at the break, with Pauric Donaghy goaling in the 22nd minute before Niall Sludden netted for the students before the break.
The college side were more impressive on the restart and had a second goal, from a Brendan Herron penalty, but the county side had enough guile to hold out for victory.
MONAGHAN: R Beggan, D Mone, F Kelly, K Duffy, M McElroy 0-1, D Hughes, K O’Connell, D Clerkin 0-2, N McAdam 0-1, S Smith 0-2, P McArdle, O Duffy 0-1, P Donaghy 1-0, C McManus 0-5 (2f), D Malone 0-1. Subs: R McNally for K Duffy, C Galligan for K O’Connell, O Lennon for N McAdam, D Hahessy for P Donaghy, S McQuillan for S Smith.
ST. MARY’S: D McAnenly, S Mullan, A Maguire, M Murray, R Loughran, C O’Hara, B Doyle, R O’Callaghan, E McCaffrey, R Sexton, B Herron 1-1 (1-0pen, 0-1f), N Sludden 1-0, D McKinless 0-4 (4f), J Johnston, J Duffy.
Subs: S O’Neill for E McCaffrey, R Johnston for B Doyle, O MacIomhair 0-1 for A Maguire.
Referee: E McHugh (Tyrone).