Cork did what they could to save themselves in Division Two, but poor results earlier in the campaign caught up with them as they earned a hollow victory in the Athletic Grounds.
It was so nearly a great escape for Cork, who showed a lot of fight to pull off a good away win over Armagh, but Clare's win in Tipp means they will be playing Division Three football next year for the first time in their history.
Armagh were already safe in Division Two and were poor in the first half and trailed by eight points at one stage, but they were much improved after the break setting up a dramatic finish in front of 3,425.
Cork led 2-6 to 0-6 at half time with two early goals from Brian Hurley the highlights of a whirlwind start when they hit an unanswered 2-3 in an eight-minute spell.
Even when Armagh drew level for the first and only time in the game through Rory Grugan's free in the 67th minute, Cork kicked on with late points from subs Cian Kiely and Damien Gore, but it was too little too late as their relegation was confirmed.
It had all looked so good for the Rebels at half time, leading by six with Tipperary leading Clare by five points in Thurles.
Hurley's first goal came in the fourth minute. He cut in along the sideline, exchanged quick passes with Mark Collins before burying the ball low to the far corner.
He skinned Paul Hughes again for the second, prompting Armagh to switch markers, with another low left-footed finish to help Cork into a useful 2-3 to 0-1 lead.
Armagh, already safe in Division Two, had little to play for and it certainly looked like that in a sluggish opening half, although Aidan Forker carved out a good goal chance which Mark White blasted over the bar.
The home side did have a good spell just before the break landing three out of four scores through Jemar Hall and Rory Grugan (two) to close the gap to six.
Cork found a lot of joy cutting Armagh open clean through the middle and Eoghan McSweeney (two), Cillian O'Hanlon and Mark Collins stroked over lovely points with the wind at their backs.
Armagh lost Niall Grimley to a black card for a foot trip in first-half stoppage time, but going down to 14 players didn't unsettle them in the early stages of the second period.
They outscored Cork by six points to one in the third quarter with Rian O'Neill, Jamie Clarke and James Morgan all brought off the bench to inject more urgency into Armagh.
O'Neill landed a free and a mark with two Grugan frees and a fisted Joe McElroy point making things interesting with Cork only scoring one point in the first 26 minutes of the second half.
Just as Armagh came to life, Cork hit back with a brilliantly-taken goal from Kevin Crowley. The Cork defender bursting through the tackle and a low finish from 21metres out.
Instantly, Armagh responded with a raiding attack and McElroy was fouled in the square, with Jamie Clarke stepping up to bury the ball low inside White's left-hand post.
Grugan's free brought Armagh level, but Cork rallied with the late points to claim a fruitless win.
Rory Grugan 0-6 (0-5fs), Jamie Clarke 1-0 (pen), Rian O'Neill 0-3 (2f, one mark), Joe McElroy, Aidan Forker, Jarly Og Burns, Jemar Hall, Niall Grimley 0-1 each
Brian Hurley 2-0, Kevin Crowley 1-0, Mark Collins 0-3 (1f), Eoghan McSweeney 0-2, Cillian O'Hanlon, John O'Rourke, Damien Gore, Cian Kiely 0-1 each
Blaine Hughes; Patrick Burns, Joe McElroy, Paul Hughes; Ryan Kennedy, Brendan Donaghy, Aidan Forker; Jarlath Og Burns, Niall Grimley; Rory Grugan, Charlie Vernon, Jemar Hall; Ethan Rafferty, Pearse Casey, Stefan Campbell
Jamie Clarke for Campbell (29), Rian O'Neill for Vernon (44), James Morgan for Hughes (51), Aidan Nugent for Casey (58)
Mark White; Kevin Flahive, Thomas Clancy, Conor Dennehy; Kevin Crowley, Tomas Clancy, Mattie Taylor; Ian Maguire, Cillian O'Hanlon; Eoghan McSweeney, John O'Rourke, Ruairi Deane; Brian Hurley, Mark Collins, Sean White
Kevin O'Driscoll for O'Rourke (26), Cian Kiely for Taylor (HT), Damien Gore for Hurley (48), Peter Kelleher for McSweeney (66), Stephen Cronin for Sean White (70)
Maurice Deegan (Laois)