Eamonn Ryan's Cork remain on course for a 10th All-Ireland crown in 11 seasons.
The Rebelettes held off a spirited second-half fightback from Galway at the Gaelic Grounds in Limerick to secure a place in the semi-finals against Kerry on August 29.
Cork were seven points up at half-time, 1-6 to 0-2, but the Westerners fought back to within a point twice in the second half.
But the Tribeswomen couldn't get close enough to the champions, suffering another big-game defeat against their opponents - Cork won the Division 1 final replay between the sides in May.
Cork could have had a couple of second-half goals too but Áine O'Sullivan rolled an effort just wide before the Beara forward saw another effort brilliantly saved by Tina Hughes.
Despite the best efforts of Geraldine Conneally and Roisín Leonard, Galway couldn't reel in the Leesiders.
And after Munster champions Kerry secured their passage to the semi-finals earlier in the evening, the scene is now set for Cork to gain revenge for their provincial final defeat.
Scorers - Cork: C O'Sullivan 1-3, V Mulcahy 0-4 (3fs), D O'Reilly, B Corkery, A Hutchings, E Scally (f), D O'Sullivan 0-1 each. Galway: G Conneally 1-1, R Leonard 0-3, T Leonard 0-2fs, N Ward, A Daly, O Divilly, P Gleeson 0-1 each.
CORK - M O'Brien; M Ambrose, B Stack, A Barrett; V Foley, D O'Reilly, G O'Flynn; R Buckley, B Corkery; C O'Sullivan, A Hutchings, A Walsh; V Mulcahy, Á O'Sullivan, R Ní Bhuachalla. Subs: E Scally for Mulcahy (41), D O'Sullivan for Walsh (46), O Farmer for Hutchings (49), O Finn for Ní Bhuachalla (56), E Farmer for Á O'Sullivan (60+2).
GALWAY - T Hughes; M Coyne, E Flaherty, Á Seoighe; S Gormelly, N Ward, S Burke; M Hoey, G Conneally; A Daly, L Ward, O Divilly; R Leonard, P Gleeson, T Leonard. Subs: A Clarke for Gleeson (30+1), B Hannon for Daly (h-t), C Cormican for Hoey (55).
Ref - G Corrigan (Down)