Barnet extended their unbeaten run to five games after a battling draw.
They started brightly and Michael Leary drilled in a low shot from the edge of the area to put them ahead.
Adam Birchall could have doubled the lead but finished weakly, and after Lewis Chalmers pounced on a loose ball to equalise, the home side dominated.
Barnet keeper Jake Cole was inspired with a string of saves, somehow keeping out Kirk Hudson's stinging drive and diving full length to deny him again.
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