Castleford 12 Bulls 20
Sammut touched down a fine pass from Kearney in the 10th minute and Burgess added a second from close range on the stroke of half-time.
Luke Gale, Bradford's creative fulcrum throughout with some excellent kicking, converted both scores to put his side 12-0 up at the break.
Castleford battered the Bulls' line for long periods in both halves but Mick Potter's men defended doggedly to keep them at bay.
Ian Millward's side scored through Josh Griffin in the 50th minute but a penalty from Gale gave the Bulls breathing space before they grabbed a late third from Kearney to cap a superb afternoon's work.
The Tigers replied in the dying embers through Richard Owen but the Bulls were already home and dry.