Both James Walshaw and Lewis Nightingale bagged hat-tricks with Richard Marshall netting the other, as the Celts recorded their biggest league win since the 7-0 hammering of Witton Albion in October 2015.
The victory puts Celtic just three points behind league leaders Lancaster City, with the Dolly Blues having played two more games.
Glossop North End moved into fourth place after a 2-1 win at Stainton Park against lowly Radcliffe Borough.
Former FC United of Manchester favourite Mike Norton proved to be the Hillians` hero with a brace in the 12th and 23rd minutes before Lewis Reilly netted a last-gasp consolation for Boro.
Bottom-markers Burscough now have only eight games to pull off a dramatic escape from the drop after losing 4-0 at Parkside to mid-table Kendal Town.
The Linnets are 13 points adrift of the safety-mark after goals from Rob Bowman after 35 and 67 minutes, sandwiched by a Sam Bailey double on 54 and 90 minutes – the second from the spot – sealed a comfortable win for the Mintcakes.
Follow us: @evostikleague on Twitter | Facebook www.facebook.com/evostikleague
Keep up-to-date with our exclusive email newsletters.
Subscribe