Nigel Starkey's side were a goal down in the first minute from Nathan Haywood and a minute later, Sam Woodhouse added a second.
Sphinx fought back and Chris O'Shea netted in the eleventh minute before Bradley Taylor equalsied on the half hour mark.
Woodhouse hit his second of the night in 51st minute and Haywood adding his second sixteen minutes later to give Kidderminster a 4-2 victory.