The Hibees came from 2-1 down to win 3-2 with goals from Anthony Stokes and David Gray in the final ten minutes of the game at Hampden Park.
Assisting both of the goals was Liam Henderson, the 70th-minute substitute.
The on-loan Celtic midfielder had to bide his time on the bench until Halliday had put Rangers ahead moments before the switch for Liam Fontaine.
Henderson told 90MinuteCynic said: "Before the game I knew I was going to be on the bench because we played Rangers in the league maybe three weeks or two weeks before the actual cup final and we played a 3-5-2 and we won the game.
"We went a wee bit more defensive against them and it worked. I might be on the bench in the cup final and I just had to be ready.
"As soon as Andy Halliday scored the goal to make it 2-1 Stubbs straight away 'Liam get warmed up'. I need to come on and make an impact here.
"One of the good things about Stubbs was he always told me, as soon as I came into Hibs, work on your free-kicks, work on your corners because if you can get that in your locker then it is a serious weapon.
"The day before a game we would do set plays and the gaffer would say 'Hendo, you go whip them in." I must have took 350 corners or more in training that season.
"I knew I was well prepared and I knew we had players who wanted to attack the ball. So I knew if I managed to get it into a good area someone would manage to get their head on it and Dave got his baldy napper onto it and it was a great header."