The Sharks, returning to the scene of their League Trophy triumph over London Towers on Sunday, scored just 13 points in the fourth quarter and only five in the last minutes as Tony Dorsey and Nigel Lloyd steered Bullets to victory.
Sheffield led 67-62 until six consecutive points from Dorsey and two from Lloyd gave the Bullets the first lead of the quarter at 70-68. Then Lloyd's three-point play put them five ahead.
Despite two late baskets from Shark's Terrell Myers, more free throws from Dorsey and Lloyd proved decisive as Bullets moved within four points of Leopards with two games in hand.
Leading scorers: Birmingham: Dorsey 27, Kirk 16, Coleman 11. Sheffield: Robinson 20, Amaechi 18, Myers 17.