However, Edwards lasted less than 15 minutes before limping off, with Smith coming back in.
Paul Musselwhite was definitely the busier of the two keepers in the first half, keeping City in the match.
City started the second half brightly, but the home side took the lead against the run of play. Hinton crossed and Danish forward Bo Henriksen turned and shot past Musselwhite to make it 1-0 to the Harriers.
Michael Branch had two good chances to get a goal on his debut while Phil Jevons put a header over, but Kidderminster kept on top, with Henriksen having further chances to add to his tally.
City line-up (4-4-2): Musselwhite; Regan, Whittle, Anderson, Edwards (Smith 15); Green, Ashbee, Keates, Elliott (Dudfield 64); Branch, Jevons (Johnson 79).
Un-used subs: Glennon, Williams.