Down led by 0-4 to 0-3 at the break, but Joe Diver and sub James Conway dominated midfield as Derry took control in the third quarter, hitting four points on the trot.
Down rallied late on to narrow the gap through Carr, Mark Poland and Arthur McConville, but Bradley, Gilligan and Gerard O’Kane nailed on further scores to ensure Derry’s progress.
Scorers for Derry: C Gilligan 0-6 (4f); P Bradley 0-2 (2f); M Lynch, C O’Boyle, G O’Kane 0-1 each.
Scorers for Down: A Carr 0-5 (5f); A McConville 0-2 (1f); D Gordon, M Poland (1f) 0-1 each.
DERRY: D Devlin, B McCallion, L Morrow, R Dillon, C McKaigue, N Forrester, SL McGoldrick, J McCamley, J Diver, B McGoldrick, M Lynch, G O’Kane, P Bradley, C O’Boyle, C Gilligan.
Subs: J Conway for McCamley, E McGuckin for Lynch, K O’Neill for Diver, A McAlynn for O’Kane, PJ McCloskey for Conway.
DOWN: M McAllister, K Quinn, D McCartan, N Brannigan, N McParland, P Turley, K Duffin, C Gough, D Gordon, A Carr, K Anderson, M Miskelly, E McCartan, K King, B Coulter.
Subs: A Brannigan for Anderson, D Turley for N Brannigan, M Poland for E McCartan, D Hughes for Miskelly, A McConville for P Turley.
Referee: P Hughes (Armagh).