The Bees were a goal down at the break, but experienced frontman Kabba smashed in a 14-minute hat-trick - the first of his senior career - before rounding off a memorable afternoon with a late fourth.
Victory keeps alive their faint survival hopes - they are now just two points behind Albion although the Brewers have three games in hand.
Bees boss Martin Allen would not single out Kabba for praise after the game, insisting it was a team effort, and the 30-year-old agreed.
"It was my first career hat-trick but I couldn`t have done it without the lads, we all pulled together," he said.
Source: PA
Source: PA