Ballyboden have qualified for the quarter-finals of the Dublin Championships.
Paul Ryan's goal with ten minutes to go gave them the breathing space they needed to finish off Brigids.
They won on a scoreline of 2-19 to 1-12.
They join Na Fianna, who were comfortable winners over Naomh Fionnbarra by 3-26 to 2-9, and Kilmacud Crokes, who beat Whitehall by 2-26 to 0-17.
Cuala, who only retained their All-Ireland crown on the 24th of March, are also in the last eight after a hard fought 1-15 to 0-14 win over Craobh Chiarain.
Meanwhile, Sean Moran has been named as the AIB GAA Club Hurler of the Year.
He helped Cuala defend their county, provincial, and All-Ireland crowns last season, and he becomes the first winner of the prize.
Corofin's Liam Silke won the football equivalent.
