Coached by former Kerry U21 selector Jerome Stack, the winners trailed 1-5 to 0-7 at half time. But the Listowel man saw his side outscore their South Limerick opponents 2-6 to 0-6 in the second half to progress.
The all-important goals came from Tom McLoughlin and Micheal Reidy.
But it was not all one-way traffic in the first-half when Patrick Murphy proved the key figure for Galbally. He finished the half with 1-2 – his goal coming in the 23rd minute. Vincent O’Connell was accurate from frees for Galbally, but Dromcollogher-Broadford kept in touch with three points from play from Ray Lynch.
It was six minutes into the second-half before favourites Dromcollogher-Broadford got in front with three successive points from inter-county man Seanie Buckley.
They were soon 1-12 to 1-6 clear and on the road to victory and now join table-toppers Fr Caseys and Newcastle West in the semi-finals.
The fourth team is Ballysteen, who beat St Kierans 0-19 to 2-9 in Mick Neville Park. The sides were level 0-6 to 1-3 at half time. Ballysteen opened with four successive points but a Darragh Treacy goal had St Kierans back in contention by the interval.
Again Ballysteen kicked another batch of successive points on the resumption, with Danny Neville, Brendan Hayes and Declan Nash all on form, but this time a penalty from Anthony Molyneaux on 45 minutes reduced the deficit 0-13 to 2-3.
The second goal spurred a St Kierans fight back but they could only narrow to a single point and it was Ballysteen that found the late scores to edge though by four points.
Ballysteen play Newcastle West in their semi-final, with Dromcollogher-Broadford playing Fr Caseys in the other.