The unlikely revival became increasingly probable in the 72nd minute when Barker got his second, after once again making a brilliant run into the box and tapping in from close range after he was left unmarked from a low cross.
BN Dons were rattled, and Tony Woods could only hope that Hove would not find the equaliser or worse, before the full-time whistle.
But in the 83rd minute Barton-Hague struck again, this time with a remarkable free-kick from distance that sailed into the box and over everyone including Barber in the Dons goal.
That sent an already rowdy Culver Road into absolute euphoria.
For the remaining seven minutes plus added time, the two teams continued to chase the game knowing a level scoreline left their fate to a penalty shootout.
But Hove had other ideas.
In the final minute of five added on, captain Matt Ahwal hit a free-kick which, after taking a deflection off the Dons wall, sailed into the back of the net past Barber, completing the most improbable of comebacks.
The final whistle brought delirious celebrations on the pitch and in the stands, where the Hove supporters had played their part in an unforgettable match.
Speaking after the game, Hove Manager, Laurance Chandler, did his best to try and sum up the game:
“It’s just amazing!” he said, “the manner in which we won it, 1-4 down at half-time, but the game was never dead for us.
“In the first-half we didn’t play the kind of football we wanted to play, with long balls over the top, so at half-time I just said to boys to remember how we play our football, with confidence and nothing to lose.
“To win our first ever trophy like that, it’s honestly just absolutely incredible!”
But at what point in that remarkable 90 minutes did Chandler start to really believe himself that there might be a chance?
“Look you should never not believe you have a chance,” he said, “If you think you can’t come back, you won’t.
“So, when we got that first goal, we had something to build on, and something to believe in!”