The Ghosts appeared finished when they trailed by 51-40 with 3 minutes, 8 seconds to play, but Anthony Lee started the comeback with a bucket with 2:59 to go.
A trio of free throws by Matt Penecale, a three-pointer by Lee, and a basket by Amir Hinton cut the deficit to 51-50 with 2:18 left, then Lee's hoop with 54 seconds left made it 53-52.
Lee had stolen the inbounds pass and scored with 40 seconds to go to give Abington its first lead since late in the second quarter.
However, Allen got loose behind the Ghosts defense and went in for a layup just seven seconds later.
Penecale was then whistled for a charge, and Anthony Richards converted both free throws after being fouled to make it 57-54 with 10 seconds left.
Jordan Neely had a chance to tie it for the Ghosts but his three-point attempt from the right wing was long.
"Our kids fight, and they never give up," Abington coach Charles Grasty said. "We got some stops and made some shots that got us back in the game late."
Lee led the Ghosts with 20 points, 16 in the fourth quarter.
Richards paced New Castle with 16.
New Castle 11 10 18 19 – 58
Abington 8 11 11 24 – 54
NC: Malik Hooker 15, Stew Allen 11, Drew Allen 9, Anthony Richards 16, Jake McPhatter 7.
A: Khari Jefferson 2, Lazaros Mackrides 5, Amir Hinton 12, Anthony Lee 20, Matt Penecale 11, Jordan Neely 2, Scott Brown 2.