Moore joined Darlington from Whitley Bay last summer
Goals from Jamie Chandler and substitute Chris Moore saw Darlington overcome a 1-0 deficit and end Kidderminster's 15-match unbeaten run.
Harriers went ahead when captain Keith Briggs fired home from 12 yards.
Chandler then turned superbly in the area before firing home to put Darlington level after the break.
And Harriers' hopes of securing a top-five place were further dented when Moore found the corner of the net after being put through on goal.
A win for Harriers would have closed the gap on Fleetwood to one point and an end to their unbeaten run which has lasted since January could not have come at a worse time.
Briggs looked to have put the hosts on course to closing the gap on fifth place after he was put through on goal by Chris McPhee's header.
But a 10-minute delay to the second-half kick off, due to a spectator collapsing and a double substitution by the visitors, seemed to alter the course of the game.
Quakers skipper Ian Miller went close to levelling the score but he managed to misplace his header from Aaron Brown's corner.
The visitors equalised when Moore, on at half time, set up Chandler to fire past Harriers keeper Danny Lewis after goog footwork in the box.
Moore then got on the scoresheet himself after being put through on goal by Marc Bridge-Wilkinson.
Harriers had chances to ensure a win at Friday's clash with Fleetwood could put them back in the play-off spots.
But they found Quakers keeper Danzelle St Louis-Hamilton in fine form as he kept out several attempts that included a ferocious Sean Canham volley.
E-mail this to a friend 
Printable version 
Bookmark with:
What are these?