Bishop Auckland breathed a sigh of relief when they won 2-1 at Bamber Bridge on Tuesday.
The result lifted them three points away from bottom of the table Trafford, and they are now just one point behind Guiseley.
Manager Brian Honour said: "Scoring first made a huge difference to us. In recent games we've had to play catch-up, but this time we stayed in control."
Phil Ross and Andrew Shingleton scored the goals in the first 20 minutes.
Honour has released striker Kevin Devine, and has signed midfielder Steve Salvin from Easington, and he played on Tuesday.
Spennymoor are now in the top eight after their 2-0 win at Guiseley on Monday, and their next two league games are at North Ferriby and Radcliffe Borough, both of whom are above them in the league. Before that they are at home to Halesowen tomorrow in the FA Trophy.
Spennymoor have been drawn at home to Bishop Auckland in the first round of the Presidents Cup, the competition for the clubs who lost in the second round of the League Cup. The game is due to be played on December 10 at the Brewery Field.
The rest of the draw is: Ashton United v Accrington Stanley, North Ferriby v Matlock or Worksop, Radcliffe Borough or Colwyn Bay v Altrincham, Runcorn or Chorley v Leek, Stalybridge v Workington, Stocksbridge or Alfreton v Eastwood or Kidsgrove, Wakefield and Emley v Farsley.
Gateshead are at home to Harrogate Town in the last 16 of the League Cup, while Whitby go to Frickley in the first round of the Chairman's Cup, the competition for the clubs who lost in the first round of the league cup.
Midweek results - Premier Division: Burscough 2 Barrow 0, Hyde 3 Accrington Stanley 3.
First Division: Guiseley 0 Spennymoor 2, Bamber Bridge 1 Bishop Auckland 2, Belper 1 Farsley 2, Leek 1 Ossett Town 0, Workington 2 Rossendale 1.
Tomorrow's fixtures - FA Trophy: Barrow v Whitby, Moor Green v Blyth , Spennymoor v Halesowen.
Premier Division: Ashton United v Marine, Gateshead v Hucknall.
First Division: Bamber Bridge v Trafford, Bishop Auckland v Matlock, Chorley v Belper, Kendal v Witton Albion, Lincoln United v Ossett Town, Radcliffe v Guiseley, Rossendale v North Ferriby, Stocksbridge v Eastwood Town, Workington v Kidsgrove.
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