The victory also ended a two-match losing streak for Kevin West's side, who finished eighth in the final Division One table, four points clear of Mary's.
The visitors' points came from a first half Gareth Logan try and two penalties from out-half and captain Barry Lynn.
As well as league points and bragging rights, the Dr. Michael Smyth Memorial trophy was on offer on Saturday afternoon. In front of a huge crowd, Terenure managed to capture the trophy for the first time ever at Lakelands, and only the second time overall, since it was first played for between the clubs in September 2001. Mary's have won it on four occasions.
Photos courtesy of Dan Wallace/www.terenurecollegerfc.com