The Dennyboys, who are eight places above Sedge in the Premier Division table, went into the lead following a goalless first half.
Mike Garrod broke the deadlock just before the hour mark and after Chris Davey doubled the visitors’ lead, Gibril Bojang pegged a goal back for Sedge to make in a tense last four minutes.
Brighouse Town continue to set the pace at the top as they held on to the leadership with a 4-0 stroll at Long Eaton United.
Tyrone Gay gave Town a second-minute lead and Tom Matthews made it 2-0 after just seven minutes.
Matthews netted a third in first-half stoppage time to kill the contest and Luke Gibson completed the scoring 12 minutes from time.
Town are still just a point above Tadcaster Albion but have two games in hand – and will be favourites to extend their lead at the summit to four points at home on Tuesday against basement outfit Lincoln Moorlands Railway.
Albion Sports did their neighbours a huge favour when they went to third-placed Barton Town and came away with a 3-2 victory.
Scott Phillips scored the only goal of the first half as Barton controlled the game up until the interval.
Albion boss Kulwinder Sandhu blasted his players at half-time and they came out for the second half fired up.
Alex Cusack levelled and Danny Facey put Albion ahead for the first time. There was then a setback when skipper Asif Hussain put through his own net but right back Elliot Holmes popped up with the winner.
Eccleshill United also faced a tough game in Division One when Rossington Main came calling at the Rapid Solicitors Stadium.
The home side ran out 2-1 victors thanks to a Connor Shefte double. The visitors had equalised through Lee Holmes but Shefte netted the winner two minutes from time.