The Clarets will play Fleetwood Town in the quarter-finals of the Lancashire FA Senior Cup.
Burnley’s reward for beating Barrow in the first round is a home tie against the Cod Army in the last eight.
Fleetwood knocked out AFC Fylde in the first round.
Meanwhile, the Clarets’ under-18s have been handed an away trip to Preston North End in the last eight of the Lancashire FA Professional Youth Cup.
Burnley beat Bolton Wanderers in round one.
Dates for both ties are still to be confirmed.