The old saying about two points being a dangerous lead became a sickening reality for Down as an injury-time goal from Ciaran Sheehan snatched victory for Cork in Newry.
Sheehan's goal in the second minute of injury-time was the last kick of the game and it condemned Down, now pointless after three games, to an unlucky defeat which pushes them closer to relegation.
Cork boss Conor Counihan was relieved to get his team's first league points of the campaign, but admitted: "If I was Down I'd be sick altogether."
An impressive Down team performance was undone by two defensive blunders in the first-half, including an own goal from goalkeeper Michael Cunningham on the stroke of half-time.
Cork were fortunate to only trail by 1-9 to 2-4 at the break, but then enjoyed their best spell of the game in the third quarter with four points in a row.
Colm O'Neill and Aidan Walsh were clinical converting long-range dead balls and the brilliant Walsh also scored 0-3 from open play.
Down regrouped from a bad 15-minute spell after half-time. Donal O'Hare scored three points during a run of five points in a row to move the Mournemen ahead again.
With time almost up, Conor Laverty's fisted point put Down two points up and on the brink of a precious first league win.
However, Man of the Match Walsh won a ball he wasn't expected to win near the sideline and released Fintan Goold, whose low ball into the square was met by Sheehan and he blasted it into the net for the ultimate sucker punch.
"It's not often the better team is beaten, but I thought that was the case today," said a gutted James McCartan. "That was probably one of the best halves of football during my tenure and apart from a couple of errors, I couldn't have asked for more.
"I still feel we're in a better place defensively than we were. All three goals were nothing to do with how we were set up, they were just mistakes, but we won't point the finger at anyone. We're all in it together."
A bad mistake by Dan McCartan allowed Paul Kerrigan to recycle the ball along the sideline and square it to Thomas Clancy to fist home Cork's first goal after 18 minutes.
A superb finish from Connaire Harrison put Down 1-9 to 1-4 ahead again in the 34th minute. Harrison easily beat Eoin O'Mahony in the air and made the room to drill a shot across Ken O'Halloran into the far corner of the net. Once again, Down's good work was undone at the other end of the field as Cunningham's own goal, when he spilled an easy catch, kept the Rebels in the game.
O'Neill pointed two lovely frees off the ground and Walsh was even more clinical from long range, converting a 40-metre free and a '45' as well as three points from play. Donal O'Hare was impressive for Down from frees and open play, top-scoring with 0-9.
Man of the match: A Walsh (Cork)
Scorers – Cork: A Walsh 0-5 (1f, 1 '45'), C Sheehan 1-1, D O'Connor 0-3 (3f), T Clancy 1-0, M Cunningham 1-0 (OG), C O'Neill 0-2 (2f), P Kerrigan 0-1. Down: D O'Hare 0-9 (6f), C Harrison 1-1, M Poland 0-2, R Mallon, P McComiskey, A Carr, K McKernan, C Laverty 0-1 each.
CORK – K O'Halloran 7; M Shields 6, E O'Mahony 5, E Cadogan 7; T Clancy 7, N O'Leary 5, J O'Sullivan 6; G Canty 6, A Walsh 9; F Goold 7, C Sheehan 8, P Kerrigan 7; M Collins 6, C O'Neill 8, D O'Connor 7. Subs: P Kissane 5 for O'Mahony (h-t), B O'Driscoll 5 for O'Connor (60), A O'Sullivan 5 for Kerrigan (63).
DOWN – M Cunningham 3; D McCartan 5, B McArdle 5, R Boyle 7; R Mallon 7, A Carr 7, P McComiskey 5; K King 5, K McKernan 6; C Laverty 8, M Poland 7, K Quinn 5; D O'Hare 9, C Harrison 8, B Coulter 7. Subs: J Johnston 5 for Quinn (48), E McCartan 5 for King (58), S McArdle 5 for O'Hare (65).
REF – M Deegan (Laois)