It will be the battle of the Bees on the last weekend of January after the draw for the fourth round was made.
Barnet shocked football by beating Premier League chasing Sheffield United away from home on Sunday.
That earned them £135,500 in prize money alone - and now they wait to discover in the TV companies will top up their total when the live games are decided in the coming days.
Caretaker manager Darren Currie spoke of his pride after his team secured the win in Sheffield.
"I can't put it into too many words - it is such a wonderful occasion for everyone,” he said.
"We had a game plan to get through the early part of the game and nullify them and we grew into it.