Tyrone fought back to earn a point from their trip to Pairc Ui Rinn and keep themselves in contention for a place in the Division One semi-finals.
Kyle Coney put on a marvellous display of finishing to end with a nine-points haul, eight of them from play.
Substitute Ronan O'Neill scored the equaliser from a stoppage time free after Cork had forged ahead with goals from Paul Kerrigan and Colm O'Neill.
Tyrone lie third in the table with eight points from six matches to date.
Tyrone started with confidence and drive, going three points up in the opening three minutes as Coney, Darren McCurry and wing back Peter Harte all found the target.
But Cork drew level in the fifth minute when Kerrigan used his pace and guile to jink his way through for a goal.
Brian Hurley slotted over a couple of quick-fire points, but Coney's third had the sides level for the fourth time in the 21st minute.
Cork scored just one point in the second quarter as the Red Hands channelled extra men back, and broke at pace to pick off quality points.
It was Coney who continued to steal the show, floating over two more gems to bring his tally to six by the halfway stage.
Cork lost wing back Tomas Clancy to a black card, and trailed by 0-12 to 1-5 at the interval.
The Rebels started the second half strongly, John O'Rourke springing through to rifle over a point, before Hurley narrowed the gap to two.
Andrew O'Sullivan stepped up his game to give Cork an edge at midfield, and they moved to within a point of their Ulster opponents when Hayes and substitute Colm O'Neill, from a free, hit the target.
Hurley nailed another placed ball to bring the sides level in the 49th minute, and three minutes later, O'Neill collected O'Rourke's pass to blast home Cork's second goal.
Michael Shields was given the job of shadowing Coney, and in a more effective defensive effort, Cork minimised the scoring threat, restricting Tyrone to just two points in the third quarter.
Substitute Barry O'Driscoll edged the Munster men into a four points lead, but the Red Hands refused to surrender, and came close on two occasions to grabbing a goal, with 'keper David Hanrahan denying Martin Penrose.
Tyrone staged a storming finish, closing the gap through Penrose, Sean Cavanagh and Coney.
And deep into stoppage time, it was Cavanagh who won the free that substitute O'Neill clipped between the posts for the equaliser.
Cork: D Hanrahan, E Cadogan, Tom Clancy, N Galvin, Tomas Clancy, M Shields (0-1), J Loughry, A O'Sullivan, F Goold, J O'Rourke (0-2), P Kerrigan (1-0), M Collins, D Goulding, B Hurley (0-5, 2f), J Hayes (0-2).
Subs: J O'Sullivan for Tomas Clancy (BC), C O'Neill (1-2, 0-0f) for Goulding, P Kelly for Cadogan, B O'Driscoll (0-1) for Galvin, C O'Driscoll (0-1) for Kerrigan, A Cronin for Hayes
Tyrone: N Morgan (0-2, 1f, 1 '45), A McCrory, R McNamee, R McKenna, T McCann, Mattie Donnelly, P Harte (0-01), C Cavanagh, S Cavanagh (0-1), C McGinley, S McGuigan, Mark Donnelly, D McCurry (0-4, 2f), K Coney (0-9, 1f), C McAliskey (0-1, f).
Subs: D McBride for McCann, R O'Neill (0-1, f) for McCurry, M Penrose (0-1) for McAliskey, C Gormley for McGinley, N McKenna for Mark Donnelly, K Gallagher for McGuigan
Referee: D Coldrick (Meath).
Football League Division 1
Dublin 3-14 2-17 Mayo
Meath 1-14 1-11 Down
Cavan 0-14 1-08 Roscommon [Breffni Park]
Football League Division 1
Cork 2-14 0-20 Tyrone
Derry 2-17 3-09 Kildare
Westmeath 0-13 2-15 Kerry
Galway 2-14 1-13 Armagh
Monaghan 0-19 0-14 Laois
Donegal 1-19 3-07 Louth
Offaly 1-12 1-13 Limerick
Sligo 0-15 2-08 Longford
Fermanagh 1-14 0-06 Wexford
Antrim 3-15 1-10 London
Leitrim 0-16 5-16 Tipperary
Clare 3-21 2-10 Carlow
Wicklow 2-14 0-12 Waterford
Division 1 quarter-finals
Laois 2-19 2-23 Clare
Wexford 2-16 4-22 Kilkenny
Limerick 1-12 1-20 Galway
Tipperary 3-25 4-19 Cork
Division 1A relegation play-off
Waterford 1-17 4-13 Dublin
Division 1B relegation play-off
Antrim 1-18 1-14 Offaly
Division 2B relegation play-off
Fingal 0-08 4-12 Armagh