Marc Joseph was out injured so Peter Taylor shuffled his side around and brought in Ryan France on right wing.
However, after just 12 minutes he was forced into making a change. Lee Marshall was stretchered off with a suspected broken leg, so on came Scott Wiseman to make his league debut at right-back.
The new-look Tigers defence went behind midway through the first half with Simon Brown finishing from Adam Murray's pass.
Stuart Green came close to equalising but hit the bar with a free kick from 20 yards, and so it stayed 1-0 at half time.
City played the second half with the wind behind them, and took advantage in the 68th minute. Stuart Elliott took control of the ball before setting up Ben Burgess to level.
They then pressed for a winner, but John Williams almost regained Kidderminster's lead when he hit the bar just before full time.
City line-up (4-4-2): Myhill; Marshall (Wiseman 12), Hinds, Delaney, Thelwell; France, Green, Lewis, Elliott; Allsopp (Walters 65), Burgess.
Un-used subs: Musselwhite, Holt, Forrester.