The other last eight ties will see Kerry host Meath, Cork will face Waterford and Armagh to play Mayo.
Armagh, Kerry, Cork and Dublin will have home advantage for the quarter-finals, which will be played on Saturday July 6, and Sunday July 7.
On Sunday, Waterford, Galway and Meath confirmed their quarter-final slots, with Dublin’s victory over Kildare ensuring that they finished ahead of Mayo on top of Group 4.
Before Sunday’s ties, Armagh, Kerry and Cork had been confirmed as winners in their respective groups.
In Group 1 on Sunday, Marion Farrelly, Emma Duggan and Meadhbh Byrne led the way as Meath did enough to see off Tipperary by 2-15 to 2-12 in Navan, Ashling Moloney scored 0-9, six of them from play, but it was not enough to save Tipperary.
In Group 2, a first half goal from Eve Power was decisive as Waterford booked their place in the last eight with a 1-10 to 0-7 victory over Donegal at Walsh Park.
And in Group 3, Galway went on a scoring spree as they ousted Laois by 7-22 to 1-5 in Ballinasloe with Olivia Divilly and Ailbhe Davoren both getting two goals to ensure progress in second place behind table-toppers Cork.
Dublin also had a comfortable win with Hannah Tyrrell scoring a hat-trick as they defeated Kildare by 4-19 to 0-9 at Manguard Park.
In the TG4 All-Ireland SFC semi-finals, to be played at Glenisk O’Connor Park in Tullamore on Saturday July 20, the winner of quarter-final between Kerry and Meath will play the winner of the last eight meeting between Armagh and Mayo.
On the other side of the draw, the victors of the clash between Dublin and Galway will play the winners of Cork and Waterford in the other semi-final.
Meanwhile, in the TG4 All-Ireland Junior Championship, Fermanagh ended Carlow’s 100 per cent record when they made the trip to Netwatch Cullen Park a winning one on Sunday, coming out on top by 1-16 to 3-4.
Also in Group A, Sligo defeated London by 1-20 to 5-3 when the sides met in Ruislip on Saturday evening.
