Kerry claimed a place in the semi-finals for the third successive year with a one-point victory, 0-11 to 0-10, over Leinster champions Dublin at St Brendan’s Park, Birr.
Dublin forward Sinéad Ahern had the chance to take the game into extra-time with the last kick of the game but she dragged a free wide from the 20 metre line.
The full-time hooter sounded as Ahern’s effort sailed wide and Kerry, beaten Munster finalists, have recovered in fine style to keep their season alive with successive victories over Westmeath and Dublin.
Meanwhile, Galway cruised past Clare by 5-19 to 2-16, with Edel Concannon hitting 1-7.
Galway’s 12-point victory at sent the Connacht champions through to a first All-Ireland semi-final since 2005.
But despite being on the losing side, Clare’s magnificent full-forward Niamh O’Dea claimed the player of the match award, having scored 1-6 of her 1-8 tally from play.
Ultimately, it was a run of 1-5 without reply immediately after half-time that saw Galway home, as a three-point interval lead was stretched to 11.
In next Saturday’s other two quarter-finals, defending champions Cork will face Donegal while Bord Gáis Energy Division 1 champions Monaghan are up against a Mayo side inspired by Cora Staunton.
Scorers for Dublin: S Ahern 0-3f, A McGuinness (1f), S Goldrick and N Hyland 0-2 each, N McEvoy 0-1f.
Scorers for Kerry: L Ní Mhuircheartaigh 0-4 (3f), M O’Connell 0-3, S Houlihan, D Corridan, P Dennehy and L Galvin 0-1 each.
Scorers for Clare: N O’Dea 1-8 (2fs), A Considine 0-6 (5fs), R Looney 1-0, N Keane and E Considine 0-1 each.
Scorers for Galway: E Concannon 1-6 (3fs), E Curley 2-0 (1-0 pen), A Clarke 1-2, A Daly 1-1, G O’Connor 0-3, G Conneally, C Hehir and L Joyce 0-2 each, E Gannon 0-1.