Cork snatched their first league win of the campaign - 3-12 to 1-17 - with an injury-time goal from Ciaran Sheehan in Newry.
Down led by two points going in the second minute of injury-time before Sheehan kicked Fintan Goold's low ball into the net.
It was a sickening blow for Down who were 1-09 to 2-04 ahead at half-time.
Further points from the impressive Donal O'Hare had Down on course until Sheehan's decisive last kick of the game.
The home team looked to be heading for their first points in Division 1 when late points from Aidan Carr and Conor Laverty put them two points ahead with time almost up.
However, the Rebels' man-of-the-match, Aidan Walsh, won a ball near the sideline and released Goold whose low shot across the square was kicked into the net by Sheehan.
The late sucker-punch was hard luck on Down, who were the better team throughout.
Down's attacking flair was undone by two dreadful defensive mistakes in the first half which gifted Cork two goals and kept Conor Counihan's men in the game.
The home side were 0-05 to 0-03 ahead after 18 minutes when the first defensive lapse from Dan McCartan allowed Paul Kerrigan to square the ball across for Fermoy's Tomás Clancy to palm the ball into an empty net.
Down recovered from the blow and continued to dominate the play.
They reeled off four unanswered points, two from play from Mark Poland and two frees from the impressive O'Hare.
Connaire Harrison then put Down firmly in control with a superbly finished goal in the 34th minute.
Conor Laverty ghosted in between two defenders out near the wing and kicked the ball into the square.
Harrison easily beat Eoin O'Mahony in the air, made the room to shoot and then drilled a shot across Ken O'Halloran into the far corner of the net.
Down looked to be heading for a comfortable 1-09 to 1-04 lead at the break, which would not have flattered them.
However, another defensive howler came at the worst possible stage for the Mourne men, on the stroke of half-time, with an own-goal from Down goalkeeper Michael Cunningham.
A high ball into the square was contested between the goalkeeper and Aidan Walsh. Cunningham had looked less than convincing during the first half and Walsh put him under just enough pressure to force him to spill an easy catch.
The loose ball came off the leg of Down full-back Benny McArdle, but it was the goalkeeper's mistake.
After all their hard work, Down's blunders meant they only led by 1-09 to 2-04 at the interval.
Cork reeled off four unanswered points at the start of the second half, in what was their best spell of the game.
Colm O'Neill hit two lovely left-footed frees off the ground and Cork's ability to convert long-range scores was crucial.
Walsh had a superb game in midfield and hit three points from play, as well as a 40-metre free and a '45.
Down struggled in the third quarter but finished strongly. They scored 0-05 without reply to go back in front with the impressive O'Hare scoring three points, including two frees.
Kevin McKernan and Harrison also scored from play and it looked like Down had done enough when Laverty raced through and fisted the ball over the bar to put Down two points ahead.
But it proved to be a dangerous lead, with Sheehan's last-gasp effort seeing the defending league champions snatch victory from the jaws of defeat.
DOWN: M Cunningham (1-00, own goal); D McCartan, B McArdle, R Boyle; R Mallon (0-01), A Carr (0-01), P McComiskey (0-01); K King, K McKernan (0-01); C Laverty (0-01), M Poland (0-02), K Quinn; D O'Hare (0-09, 0-04f), C Harrison (1-01), B Coulter.
Subs used: J Johnston for Quinn (48 mins), E McCartan for King (58), S McArdle for O'Hare (65).
CORK: K O'Halloran; M Shields, E O'Mahony, E Cadogan; T Clancy (Fermoy) (1-00), N O'Leary, J O'Sullivan; G Canty, A Walsh (0-05, 0-01 '45', 0-01f); F Goold, C Sheehan (1-01), P Kerrigan (0-01); M Collins, C O'Neill (0-02, 0-02f), D O'Connor (0-03, 0-03f).
Subs used: P Kissane for O'Mahony (half-time), B O'Driscoll for O'Connor (60 mins), A O'Sullivan for Kerrigan (63).
Referee: Maurice Deegan (Laois)