David Carvill and Declan Coulter were the star performers at Sancta Maria College as their combined total of 1-12 paved the way for Armagh's comfortable victory.
Niall Arthur put Pat's ahead, but points from John Corvan, Carvill and Coulter, and a goal from James King, moved Armagh into a six-point lead.
Conor Joyce's goal reduced the gap, but a points blitz and a goal from Carvill made it 2-12 to 1-5 at the break.
Although the students reduced the deficit to six, Armagh then hit five unanswered points to seal their victory.
Scorers – Armagh: D Carvill 1-5 (3f), D Coulter 0-7 (7f), J King 1-1, R Gaffney, M Lennon 0-2 each, J Corvan 0-1. St Patrick's, Drumcondra: N Arthur 0-5 (3f, 1 '65'), C Joyce 1-0, D M Carroll, D Kennedy, D Wright, N Maguire, P Murphy 0-1 each.
ARMAGH – S Doherty; C McKee, C Clifford, C Devlin; N Greene, N Curry, S Gaffney; J Corvan, K McKernan; J King, R Gaffney, P Hughes; F Bradley, D Coulter, D Carvill. Subs: C Carvill for Greene (h-t), M Lennon for Hughes (h-t), R Fullerton for King (47), B Mallon for Devlin (47), B Breen for S Gaffney (54).
St Patrick's, Drumcondra – S Russell; D Glynn, D Fitzgerald, N Unwin; J Kelly, P Butler, D M Carroll; D Kennedy, R Peacock; C Spollen, D Wright, F Walsh; N Arthur, C Joyce, E Dunphy. Subs: P Murphy for Spollen (25), N Maguire for Dunphy (h-t), E De Barra for Unwin (h-t), C Caufield for Peacock (48), A Keogh for Walsh (53).
Ref – G McGrath (Setanta, Dublin)