Mayo beat 2010 All-Ireland football champions Cork 1-13 to 2-6 to set up a semi-final meeting with Kerry.
Cork led 1-4 to 0-1 after netting a penalty through Donncha O'Connor.
Kevin McLoughlin hit back with a goal for Mayo while Paul Kerrigan netted the second for Cork who managed just one point after the interval.
Kerry cruised into the semi-finals by beating Munster rivals Limerick 1-20 to 0-10, Darran O'Sullivan getting the goal with a back-heeled effort.
In the other semi-final, Ulster champions Donegal will take on the winners of Dublin's meeting with Tyrone.