A solid start from goalkeeper Mark Jepson kept Billinge in the game early on before The Clarets were knocked off their stride with a shoulder dislocation for Anthony Farrell.
However the lads are made of stern stuff and rallied to become firm winners in incredibly testing conditions.
Stand-out performances came from Ben Reece, young Adam, Jason Newell, Geoff Parr and Elliot while the man-of-the match went to Danny for a commanding performance in centre midfield.
The goal scorers for Billinge were Chris Cullen, Aaron Bailey and Dan Hague.