Second half goals from Jonathan Oglesby, Luke Mascall and Brody Robertson saw the Owls claim all three points.
Manager Marcus Newell kept with the same line-up from last weeks 1-1 draw with Handsworth Parramore.
The Owls made a good start to the game and were on top from the get go. Mascall nearly opened the scoring with just seven minutes on the clock as Rob Zand denied the winger with a great stop.
Just five minutes last Zand was on hand once more, this time to deny leading scorer Marc Cooper then Kieran Wressell both from close range.
Shots kept raining down on the Barton goal as Oglesby, Cooper then Robertson were all denied by Zand who looked like he was "having one of those nights".
However, just six minutes after half time, the deadlock was finally broken when Oglesby nipped in ahead of Zand to finish into the bottom corner sending the traveling fans into delirium.
Only 15 minutes later and the Owls had further increased their lead as Mascall headed home from close range.
The game was put beyond any doubt just 45 seconds later as Robertson pinched the ball back from the kick-off and his shot from just outside the area nestled into the bottom corner sealing a comfortable win for the Owls.
The win puts them back up to fourth in the table, just three points behind leaders Tadcaster Albion.