Mickey Demetriou's late equaliser moved Kidderminster off the foot of the table as they drew at Braintree.
Both sides hit the woodwork, Richard Peniket heading against the bar for the visitors and Michael Gash drilling a shot against a post at the other end.
Dan Holman netted his fourth goal in three games with a curling 12-yard effort to put the hosts in front.
But Demetriou's 20-yard shot into the top corner secured Harriers their second point of the season.
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Braintree manager Alan Devonshire told BBC Essex:
"First half, we could have gone in maybe two up, but I'm not going to knock them.
"We've had three tough games in seven days, I kept the same side and they got tired, you could see it.
"That's probably the part-time thing coming out - we're playing full-time teams in this league - but they gave me everything and I can't ask any more as a manager."