Ryan Woodford celebrated his 200th Hawks appearance by heading them into the lead five minutes before half-time.
The Tudors equalised from the penalty spot, though, eight minutes from the end, after a foul by goalkeeper Ryan Young.
Striker Matt Tubbs was given his first start since returning from a month’s loan spell at Weymouth.
One other change saw Theo Widdrington replace Andreas Robinson, who dropped to the bench.
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Widdrington was denied by an acrobatic save from the Tudor’s goalkeeper, Laurie Walker, in the opening three minutes.
Rory Williams was involved twice in a short corner routine before Walker turned Widdrington’s volley over the bar.
On 16 minutes Widdrington curled a 25-yard free-kick narrowly over the top. Another good chance went begging when Bradley Tarbuck blazed over from Prior’s first-time cross.
On 34 minutes the Hawks had an escape when visiting captain Jordan Parkes burst clear but under pressure put his shot over.
Walker produced more acrobatics to turn a powerful rising drive from Wes Fogden over for a corner.
The Hawks broke the deadlock from the resulting 40th-minute corner.
Ryan WOODFORD marked his 200th appearance for the club with a far post header from a corner.
Tubbs tested Walker with a shot from the edge of the area in the opening minutes of the second half.
The Hawks went close when Dan Strugnell thumped a powerful header wide of the post from a corner.
Fogden should have scored when put clean through, but under pressure he put his shot the wrong side of the post.
The home side looked in control as they searched for a second goal to kill the Tudors off.
There was huge let-off for the hosts when Ismael Yakubu headed over from point-blank range from a corner.
On 83 minutes PARKES equalised with a penalty after Young felled a Tudor forward in the area.