Robert Emmetts hit three points in as many minutes at the end of extra-time to book a semi-final date with Carrickshock.
Antrim side St Brigid's Cloughmill were stunned after the Londoners equalised in the second minute of added time to send the game into extra-time.
Emmetts' strength in depth eventually proved the difference but Richie Murphy's shooting from frees was crucial for the hosts.
The sides were deadlocked at 0-5 apiece at half-time and the second half was tight too, Murphy making it 0-10 to 0-10 with an injury-time free.
Geoffrey Og Laverty and Owen Kinney both missed chances to win it, while Murphy also missed a long-range free as the game headed for two added periods. Murphy's 12th point put them three points to the good but Michael Devlin went close to forcing a replay, his late free whizzing over the crossbar.
Scorers - Robert Emmetts: R Murphy 0-12 (12f), T Lawrence, D Roberts 0-2 each. St Brigid's Cloughmills: M Devlin 0-9 (7f, 1 '65), L Kearns 0-3 (3f), S Smyth 0-2.
Robert Emmetts - S Ryan; M Conroy, S Griffey, C Walsh; T Healy, P Horkan, P Breen; T Lawrence, M O Laodha; E Kenny, R Murphy, K Morrisey; D Roberts, E Kenny, C Keogh. Subs: D Regan for O Laodha (38), F McMahon for Breen (43), M Dwyer for Keogh (52), E Chawke for Kenny (52), M Fitzpatrick for Morrisey (57), Kenny for Healy (68), Morrisey for Regan (76).
St Brigid's Cloughmills - C McKiernan; S Martin, JB McGuckian, S McKendry; M Morrison, A Smiley, R Laverty; C Laverty, M Devlin; L Cassley, J Doherty, S Smyth; G Og Laverty, O Kinney, L Kearns. Subs: M Dobbin for Cassley (h-t ET), J Smyth for Laverty (73).
Ref -J Keane (Galway)