The Tipperary school, who were beaten in the Dr Harty Cup Final two weeks ago, defeated Gort CS 1-18 to 0-14 to book their place in the last four.
Our Lady's goal was scored by captain Anthony Ryan.
However, the skipper will miss the semi after being sent off late in the game, which was played in Kilmallock.
The Tipp school will face St Kieran's Kilkenny in seven days' time.
