Brighton went agonisingly close to breaking the deadlock in the sixty-seventh minute when Tilley smacked a powerful effort against the crossbar, but it was Crawley who found the breakthrough just seconds later.
Boldewijn’s marauding run out wide allowed him to drill a dangerous ball into the area which Kerr diverted into his own net.
As the game entered its closing stages Crawley looked as if they were going to hold on and win the competition for the first time in thirteen years, but Tilley’s leveller in the eighty-second minute changed the complexion of the match.
A defensive mix-up allowed Bojan Radulovic to feed the Albion midfielder to slot past Yusuf Mersin from close range.
Brighton, revitalised by the goal, immediately pressed for a second. Less than a minute later Tilley had a chance to double his tally from the penalty spot, but Mersin saved brilliantly to deny him another.
However, the elusive winner arrived from the resulting corner, with Kerr climbing highest to head home and break Crawley hearts.
Brighton boss Rusk praised his side’s character after the match: “I was really pleased with the performance tonight, and the levels of resilience.
“It’s a trophy that at the start of the year we wanted to go and win, and thankfully, down to the players’ commitment we managed to get the win,” he said.
Meanwhile, Crawley manager Kewell congratulated his opponents on the victory: "We knew they [Brighton] are a young team, they had the energy and they were up for it.
“People want to see us go places, but I think we need to sit down and have a look at bringing some fresh faces in [ready for next season].”