Nathan Elder ensured Ebbsfleet claimed a point against fellow Blue Square Bet Premier strugglers Kidderminster.
Anthony Malbon put Harriers ahead midway through the first half when he fired in from inside the area.
But Elder levelled for the Fleet soon after when he headed in from Louie Soares' corner.
Harriers are unbeaten in eight games but have only won twice so far this season while Ebbsfleet are two points behind them and second from bottom.
VIEWS FROM THE DRESSING ROOM
Ebbsfleet manager Liam Daish told BBC Radio Kent:
"I was happy with the performance, the lads really worked hard, we could have been coming in 2-0 up, maybe more, but the lads put in a lot of effort.
"We showed togetherness, defended properly, we haven't got the full three points but the performance has given me something to think about that we've competed really well.
"It's about taking chances, we went a goal down, but we stuck in there and scored a great goal.
"After the week I've had personally, the performance has pleased me."