After losing at Macclesfield Town in midweek, Barnet started the game strongly and could have taken the lead on several occasions during the opening stages only to have Harriers goalkeeper Daniel Lewis keep them out.
As the half progressed, Sam Hoskins, Luisma Villa and Andy Yiadom all had opportunities to break the deadlock, but the Bees finally found the back of the net on 32 minutes when Villa curled home a free kick from 30 yards.
Six minutes later, the lead was doubled when Lee Cook's delivery from the right flank evaded everyone before finding the far corner to put Martin Allen's team in full control as the game approached the break.
It got even better for the home side two minutes before the interval when John Akinde drifted in between goalkeeper and defence to slot home and almost put the game out of Kidderminster's reach.
However, 13 minutes into the second half, Kidderminster reduced the deficit as Michael Gash volleyed in from close range at the back post, but the striker seemed to have handled when controlling the ball.
Either side of the goal, Barnet made alterations to their side, potentially with the thought that the game was over, but Kidderminster were much improved from the first half and regularly pushed forward.
However, they did make it 3-2 with 10 minutes remaining when Nathan Blissett rose highest to head home from close range to ensure a nervy finish at The Hive Stadium.
Blissett was proving to be a handful for the Barnet defence and two minutes later, he completed the turnaround for his side when he sent another header into the net after being found by a corner.
Gash very nearly earned Kidderminster an unthinkable win in the closing stages but, after his header was tipped over by Stack, both teams had to settle for a point after an enthralling 90 minutes.