Cork recovered from a poor opening round defeat by Tipperary to pick up their first Allianz League points in Newry.
A strong second-half performance, outscoring the home side by 1-06 to 0-04 including a 55th minute goal by Mark Collins, saw them extend their two-decade long unbeaten run against Down.
Both sides finished with 14 players with Cork's Jamie O'Sullivan and Down's Connaire Harrison sent off after a scuffle right on the stroke of full-time.
The first half was competitive, Cork led by 0-05 to 0-01 after 13 minutes with Colm O'Neill, Mark Collins and Sean White all on target.
However, Caolan Mooney was Down's saviour, getting the Mournemen back into it with a sparkling display.
Anthony Doherty's long-range free-taking off the ground was also huge for Down and they battled well to reduce the deficit to 0-07 to 0-06 at the break.
Cork's six-point home defeat to Tipperary last week may have been a wake-up call and certainly, their need for the Division Two points on offer was greatest, and they were the only team in it in the second half.
Down had put themselves in a decent position in the second quarter but there was no spark about them after the break as Cork took control.
Down drew level six minutes after the restart through Shay Millar, but two quickfire points from Collins, one a free, edged them ahead midway through the second half.
While a long-distance effort from Mooney closed the gap to 0-09 to 0-08 on 53 minutes, Collins' goal in the 55th minute killed Down off.
It all came from an awful kick-out by Shane Harrison that went straight to Ruairi Deane. He played in Collins who spotted the Down keeper off his line and cleverly looped the ball over his head and into the net.
O’Neill then added a free to put Cork in a 1-11 to 0-8 lead with 12 minutes remaining, and it was all over as a contest.
Having beaten Louth last week, Down found Cork a big step up in class.
The return of experienced duo Kevin McKernan and Ryan Johnston, who both scored late on, was a positive at least and both will be crucial throughout what looks a difficult Division Two campaign.
Down: S Harrison; C Flanagan, D O’Hagan, B McArdle; D O’Hanlon 0-02 (2f), N McParland, A Doherty 0-03 (3f) C Poland, N Donnelly; C Mooney (0-01), C Maginn, S Millar (0-01); D O’Hare, C Harrison (0-01), A Morgan
Subs: B O’Hagan for O’Hare (51mins), K McKernan (0-01) for Maginn (51mins), R Johnston (0-01) for Millar (56mins), D McKibbin for Doherty (56mins)
Cork: M White; S Ryan, J O’Sullivan, M McSweeney; K Flahive, B O’Driscoll, T Clancy; I Maguire, C O’Hanlon; S White (0-02), K Crowley, R Deane; J O’Rourke, C O’Neill (0-5 4f), M Collins (1-05 2f)
Subs: M Hurley for O’Rourke (44mins), C Dorman for O’Driscoll (51mins), P Kelleher (0-01) for O’Hanlon (60mins), M Taylor for White (63mins), C Dorgan for Flahive (68mins), S Sherlock for O’Neill (69mins)
Referee: Fergal Kelly (Longford)