Thomas CostelloE scored one try and made the other as Gonzaga College defied difficult conditions at Anglesea Road to advance to the quarter-finals.
Terenure enjoyed the majority of possession and territory but failed to capitalise on the few try-scoring opportunities they created. Harry Kavanagh also missed two penalties from in front of the posts, leaving Gonzaga the happier side at the interval.
And they took the lead six minutes into the second half when Costelloe scored in the left-hand corner after good work from the forwards.
A second try arrived via Jack McNamara not long after. Terenure full-back Ronan O'Hare saw his kick expertly charged down by Costelloe and the flanker was on hand to score.
The Gonzaga defence stood firm to secure a well-earned victory.
TERENURE – R O'Hare; J Carroll, T O'Donoghue, H Kavanagh, D McQuerins; M Fabian, C Cahill; J Dignam (c), J Clarkin, S Patchell (J Lynch); J Byrne, C Coughlan;S Collins (Z Vaughan), J Henry – Haye, K Smith (J Boyden).