Darren Fletcher's side progressed past West Ham United at the last-four stage, with a 3-1 win, at Carrington last week.
Gabriel levelled for the Reds in the first half and, after it remained 1-1 after 90 minutes, extra-time strikes by Nathaniel-Junior Brown and Rooney earned victory for our youngsters.
Palace, who defeated Tottenham Hotspur in the semi-finals, will be at home as the two sides compete to lift the trophy.
The game is to be staged at Selhurst Park on Wednesday 22 April, kicking off at 19:00 BST.
The final must be settled on the night, with extra-time and penalties, if required.