Cork ended All-Ireland champions Dublin’s involvement in this year’s league and booked themselves a place in the last four with a three-point win at Pairc Ui Chaoimh.
The result means the Rebels will face Down in the semi-final stage of the league, while Pat Gilroy’s men are out of contention.
Conor Counihan’s charges led by six at the break, 1-8 to 0-5. Colm O’Neill and Paul Kerrigan his two apiece in the first half and Aidan Walsh bagged 1-1. Diarmuid Connolly notched two for the lethargic Dubs before the interval.
The Rebels roared into an early lead thanks to Donncha O’Connor and roving full forward Aidan Walsh.
Walsh flicked the ball to the net to make it 1-5 to 0-1 in Cork’s favour after 20 minutes and that goal ultimately proved the difference between the sides as the Rebels fought off a late Dubs comeback.
Elsewhere, Down doomed Laois to relegation with a 2-11 to 0-10 in Portlaoise and booked their place in the last four in the process.
Conor Laverty’s goal gave the victors a 1-5 to 0-5 interval advantage.
Colm Begley pointed in the second minute of the second half to close the gap to two.
But Coulter goaled in the 10th minute of the second half to put Down 2-6 to 0-6.
There was no way back for Laois from that hammer blow l and they will be playing Division 2 football in 2013.
Donegal secured their own top-flight status and send Armagh down with a 0-13 to 0-10 win in Ballybofey.
Armagh looked to have done enough when leading by 0-10 to 0-7 but Donegal finished strongly with a stirring run of six unanswered points to send the Orchard men down.
Aaron Kernan and Jamie Clarke started for the Orchard County, who led by 0-7 to 0-5 at the interval.
Stevenson added two more frees to double the gap after the action recommenced but Donegal then took over.
Frank McGlynn, McFadden, substitute Martin O’Reilly and Rory Kavanagh bagged four in a row for the home team and they powered on to victory from there.
In the weekend’s other top-flight game a draw in Tralee meant Kerry and Mayo will meet again in a league semi-final.
Mayo were 1-8 to 0-7 to the good at the break but Jack O’Connor introduced supersubs Paul Galvin and Darran O’Sullivan during the break and they led the fightback for the semi-final bound Kingdom.