The cup holders had an 24-19 win over Old Belvedere at Anglesea Road on Sunday and meet a Lansdowne side who accounted for Junior qualifiers Kilkenny 28-13 at Merrion Road.
Last year's beaten finalists Clontarf are at home to De La Salle Palmerston, Bective Rangers play Trinity in College Park and biggest crowd of the round can be expected to assemble in Oak Park where Co. Carlow will take on St. Mary's College.
Full Draw.Co. Carlow v St. Mary's College; Clontarf v D.L..S.P.;Terenure College v Lansdowne; Dublin University v Bective Rangers.
Matches will take place on Sunday 18th November, Kick offs 2.30pm.