But Club moved above the Blues into eleventh after this victory which saw Marc Newsham score twice in 3 minutes around the half-hour mark to give the visitors a cushion.
Tyler Walton pulled one back for Frickley in the 34th minute, but less than 2 minutes later, Mitch Dunne restored Club's two-goal advantage.
Jacob Hazel did manage to pull a second back for the home side right on the stroke of half-time.
However, the second half was disappointing and saw no further goals.
Tuesday's only other league game saw bottom-markers Cleethorpes Town earn a point from their visit to the Fens to play Wisbech Town.
Jon Fairweather gave the Fenmen a 20th minute lead that Scott Vernon cancelled out just 7 minutes later.
Report courtesy of Steve Whitney from Non League Today
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