The Bulls were still in control of the game at that point but failed to take advantage of their pressure on the home side’s try-line.
Instead it was the Airlie Birds who added the second try, a perfectly weighted Horne kick from the scrum base allowing Motu Tony to race in for a superbly crafted touch down; and Paul Cooke added a drop goal to put Hull 13-0 up at the break
The Bulls dragged themselves back into the contest with a try from Brett ferres shortly after the half time interval.
But the hosts added a further try from Kirk Yeaman to put them in the driving seat for the remainder of the game, with Jamie Langley’s late try not enough to stop them from progressing to the Old Trafford final.
Hull boss Peter Sharp could not convey his feelings in words after the win, but was able to congratulate his players for their achievements.
"I'm a bit lost for words to be honest," he said. "It was a magnificent defensive effort which set the platform for the win.
"Everybody contributed but there were some great individual performances, which there needed to be against a quality side like Bradford."
Bradford coach Steve McNamara admitted that the loss was a tough one to take, but added that he was proud of his players’ efforts.
"It's been a really tough week for us but the players responded magnificently," said McNamara. "I can't speak highly enough of them.
“If I'm honest, it hurts like hell but I'm proud to be associated with that bunch of players. We pushed hard but didn't quite get there. We missed some opportunities and when you do that it tends to come back and bite you.
"There is a fine margin between a victory and a loss."