The home side were looking to keep the pressure on Conference leaders Oxford, who they meet next Saturday in the FA Cup.
Meanwhile, Kidderminster were looking to bounce back after being soundly beaten by Aldershot last time out.
It was the home side who made all the early running and it was no surprise that the Dagenham strikeforce of Paul Benson and Craig Mackail-Smith combined to give the promotion chasers the lead.
Benson released Mackail-Smith who easily skipped past Kidderminster defender Mark Creighton and coolly slotted the ball past the on-rushing Keeper Scott Bevan for his fifth goal of the season
Their advantage could have been doubled on nine minutes when Bevan made hard work of a Glen Southam free-kick which struck the keeper's chest and rolled round the post for a corner.
The Harriers, who have scored just 11 league goals all season, went close with a Craig Nelthorpe near-post corner met by Creighton who headed over and should have done better.
Minutes later the visitors carved out the first real chance when Reuben Reid combined with Iyseden Christie, but he shot tamely over the bar from 20 yards out.
Kidderminster started to come back into the game with some decent approach play, especially from the lively Michael Blackwood who made some penetrating runs down the left flank.
Moments later Mackail-Smith should have doubled his side's lead when some neat work on the flank allowed Danny Foster to swing in an excellent cross but the unmarked Mackail-Smith headed wide from 12 yards out.
Kidderminster came out for the second half with all guns blazing and should have got back on level terms when Nelthorpe crossed for Christie, but his weak header went wide.
Scott Griffiths could have given his side the two-goal cushion they needed when he cut in from the left flank but drilled his shot straight at Bevan
On 54 minutes the Harriers got the equaliser their play deserved through Simon Russell after he was first to react to Gavin Hurren's shot which cannoned back off the post.
Kidderminster were in the ascendancy and could have taken the lead a minute after they equalised when Hurren again ghosted into the Dagenham box, but his close range effort was cleared off the line by Southam.
Kidderminster were now by far the better side with Reid and Christie at last showing some pace and enterprise to cause the Daggers defence plenty to think about.
On 71 minutes the visitors took a deserved lead when the impressive Blackwood went on another one of his long runs, clipped the ball into Christie who sent Reid through and he smashed the ball into the roof of the net to send the away fans into dreamland.
On 88 minutes Harriers sealed the three points their second-half display deserved when the impressive Christie flicked on a clearance which sent substitute Andy White clean through and he calmly placed the shot under keeper Tony Roberts.