The six-year-old, trained by Richard Fahey and ridden by Tony Hamilton, defied Mull of Killough to win by a short head at 25-1.
Fury was third a length back, with Edinburgh Knight finishing fourth ahead of favourite Eton Forever.
Brae Hill took up the running two furlongs from home and demonstrated huge strength to hold off the challengers.
"He is still very wooly to look at but he stuck his head down all the way to the line. I did think I had won, even though it was only a short head," said Hamilton.
Fahey was thrilled to record a first victory in the race.
"I've been trying to win this race for years and never thought I would. I've been second, third and fourth in it so many times so it's nice to win it," he said.
"This is a prestigious handicap and a nice one to have on your CV."
Fahey added that he had total faith in his jockey despite having lost number one rider Paul Hanagan to Sheikh Hamdan's stable.
"It's fantastic for Tony," said Fahey. "Everyone keeps asking me who'll be my new stable jockey but I've already got some very good jockeys at home. Tony Hamilton is as good a rider as you'll get so I've got no worries about jockeys."
1. 15 Brae Hill 25/1
2. 14 Mull Of Killough 10/1
3. 10 Fury 8/1
4. 1 Edinburgh Knight 11/1