The pair came into the weekend level on 32 points, 10 adrift of runaway leaders Radcliffe who were in FA Trophy action on the same day.
Despite falling behind to a 41st-minute Vaughan Redford penalty, Ben Hardcastle equalised on the stroke of half-time for the Blues before Adama Sidibeh netted a late winner for the second Saturday in a row.
Elsewhere, Guiseley missed the chance to climb up to fourth as a dramatic stoppage-time penalty from Declan McLoughlin helped FC United of Manchester to a thrilling 3-2 win at Broadhurst Park.
Morpeth Town, meanwhile, moved into the top half of the table as a Sam Hodgson double steered them to a 2-1 victory over Ilkeston Town.
Goals in either half proved enough for Whitby Town as they ran out 2-0 winners at home to Bamber Bridge - a result which means the Seasiders end the weekend 11th.
The Brig, beaten in last season's play-off final, have now won just one of their last six matches in all competitions.
A second-half double from David Symington helped Workington to a comfortable 3-0 win at Basford United, and Gainsborough Trinity extended their recent resurgence as quickfire goals from Dayle Southwell and Javelle Clarke saw them recover from a goal down to clinch all three points against Bradford Park Avenue at Northolme.
The other scheduled games on Saturday afternoon - Atherton Collieries against Marine and Lancaster City's trip to Marske United - were both postponed due to a waterlogged pitch.
Results - Saturday 18 November
Atherton Collieries P-P Marine
Basford United 0-3 Workington
FC United of Manchester 3-2 Guiseley
Gainsborough Trinity 2-1 Bradford Park Avenue
Marske United P-P Lancaster City
Morpeth Town 2-1 Ilkeston Town
Warrington Rylands 2-1 Worksop Town
Whitby Town 2-0 Bamber Bridge
Photo credit: Warrington Rylands