Andy Morrell's strike on the stroke of half-time ensured second-placed Wrexham kept the pressure on Blue Square Bet Premier leaders Fleetwood.
The Wrexham player/manager found the bottom corner from close range to secure a 10th win in 11 league games at play-off chasing Kidderminster.
Neil Ashton's free-kick in first-half injury-time was not cleared and Morrell poked in his 10th goal this term.
Jake Speight and Mathias Pogba could have extended Wrexham's lead.
Harriers had their chances, midfielder Jack Byrne heading Nick Wright's inswinging corner over the bar from close range, while Steve Guinan also headed wide.
But the Welsh side hung on for a battling 1-0 victory to maintain their promotion challenge.
but Wrexham, who are two points behind the table-toppers, have a game in hand.
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Kidderminster manager Steve Burr told BBC Hereford and Worcester:
"They are a good side but I thought we pushed them all the way, we took a different approach to the game tonight to get in amongst them
"It worked to a certain degree, but little things you need to drop for you have deserted us at the minute.
"We didn't create enough in the final third but the lads worked their socks off tonight."
Wrexham player/manager Andy Morrell told BBC Radio Wales:
"We went a bit deep in the second half, but we didn't have great deal of energy so I'm pleased to have hung on.
"The clean sheet is paramount. We were disappointed not to get it on Saturday but we got it tonight.
"They are a good outfit, Kiddy, really tough team to play against. And it's not many team that will come here and beat them."