Mayo joined Tyrone, Dublin and Kildare in the Allianz Football League Division 1 semi-finals.
The Connacht champions edged out Cork by 11 points to 10 at Pairc Ui Chaoimh.
Kerry avoided relegation thanks to a 1-16 to 2-12 win over Tyrone in Omagh.
It means All Ireland champions Donegal go down after a draw with Dublin.
Down will also play in Division 2 next season despite a 3-13 to 1-12 win over Kildare.
Dublin will play Mayo in the semi finals while Kildare will face Tyrone.
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Derry secured promotion to the top flight with a 2-17 to 1-5 win over Westmeath.
The two sides will meet again in the Division 2 final.
Louth beat Longford by 1-14 to 1-8 which means Longford are relegated along with Wexford who lost to Laois by 14 points to 1-8.
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Monaghan and Meath were promoted from Division 3 while Wicklow and Antrim go down.