Chester took the lead just five minutes in as Keenan Quansah failed to clear the ball after a corner, with Dylan Mottley-Henry teeing up Finley Shrimpton to score.
But Hereford started to click as a team and pulled themselves back level as Lewis Hudson's long ball was well controlled by George Munday, laying off to Justin Donawa to equalise.
The Bulls then took the lead as Aaron Skinner's run down the right saw a number of players combine well, with the ball eventually falling to Cormac Daly to convert.
But the lead didn't stay intact for long as Chester scored their second from the spot courtesy of Connor Woods, though a near immediate reaction from Hereford saw Keziah Martin restore the one-goal lead before the break.
Half time: Hereford 3 - Chester 2
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