Down missed out on a place in the NFL Division One final as Cork won by eight points to go through to meet Mayo.
Cork held a two-point lead at half-time and pulled further ahead when Colm O'Neill shot in their first goal in the 43rd minute.
An Aidan Carr penalty threw the Ulster county a lifeline after a defender had handled the ball on the ground to prevent a goal.
However, Alan O'Connor got Cork's second goal on 60 minutes.
O'Connor was gifted the simple chance of netting from close-range after Down keeper Brendan McVeigh dropped a high ball.
It was a disappointing end for James McCartan's men who had been well in the contest for most of the game.
They held an early 0-3 to 0-1 lead after points from Arthur McConville, Conor Laverty and Benny Coulter.
Laverty added two more with Mark Poland and Brendan McArdle also pointing for Down, but Cork, with Colm O'Neill, Paul Kerrigan and Pearse O'Neill prominent, led by 0-9 to 0-7 at the interval.
Substitute Conor McGinn, Coulter and Aidan Carr scored early in the second half as Down cut the gap to just one point.
Barry O'Driscoll restored the two-point gap before Colm O'Neill drilled a low left-foot shot past McVeigh for the opening goal.
Carr's confident penalty conversion left Down just 1-13 to 1-11 in arrears.
Noel O'Leary and Carr exchanged points before Cork settled matters with O'Connor's goal with 10 minutes left.
Colm O'Neill and substitute Daniel Goulding added points to leave 2010 All-Ireland champions on course for a hat-trick of league titles.