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Striker Nathan Elder broke the deadlock in the 66th minute at Edgar Street on Saturday when he headed home his first goal for the Bulls.
Barnet went close to breaking the deadlock in the League Two clash in the 17th minute when a powerful 20-yard shot from Mark Holmes was tipped over the crossbar by David Cornell.
Goalkeeper Cornell also saved from Mark Hughes and Izale McLeod as the Bees stepped up a gear.
Liam O'Brien kept the Bulls at bay for a while, saving a Steven Leslie strike, but Richard Featherstone swept in a corner to Elder who headed past the Bees' goalkeeper from close range.
One minute later, only a block from Hereford skipper Stefan Stam stopped Darren Dennehay equalising for Barnet.
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