With Morpeth Town out of action, they both won by a solitary goal away from home.
Joe Lumsden struck for Taddy in a 1-0 win at Carlton Town, while Mohammed Ibrahim was the matchwinner for Brighouse at Gresley.
AFC Mansfield earned a rare point as they held Marske United to a goalless draw, a result which has them edge a point closer to Stocksbridge Park Steels, who were beaten 1-0 at Stamford through Ryan Seal’s goal.
Cleethorpes Town made it four wins from six as they beat Spalding United 2-1. Kieran Wells cancelled out Josh Batty’s first half opener, but Scott Vernon struck the winner 11 minutes from time.
Sheffield sit within three points of the play-offs after plundering five goals past lowly Pickering Town.
Luke Rawson and James Gregory (2) had them 3-0 up by the break, and though Ryan Blott pulled one back, Mitchell Dunne and Jamie Yates sent them in to Christmas off the back of a five star display.
Jacob Hazel continued his fine run of goalscoring form with the equaliser as Frickley Athletic drew 1-1 with Wisbech Town, Sam Gaughran scoring their goal.
And in the only other game of the day, Ossett United drew 1-1 at home to Loughborough Dynamo.
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