They seemed to have set out their stall as early as the fifth minute when Ben Burgess' six-yard shot was held by keeper Stuart Brock who then lost his balance and fell over the line with the ball still in his hands.
But City began to lose their shape and gradually let the Harriers back into the game.
The visitors deservedly drew level after 21 minutes when a mistake by Damien Delaney let in John Williams who rolled in a 20-yard daisy cutter past Musselwhite for what was an equally soft goal.
City continued to play deep and let Kidderminster play, and it wasn't until the 43rd minute that they got back on the road to recovery after Brock had excellently palmed away a point-blank header from Price. Danny Allsopp pounced on a loose ball and swung in a shot from 15 yards.
Just after the restart Allsopp was to have another goal disallowed, before City put the game beyond doubt with Dawson's brilliant solo effort on the 58th minute. The Tigers defender controlled the ball squared up and placed a 30-yard screamer into the back of the net.
The Harriers, were by now, already defeated and were largely anonymous and when they failed to clear the ball eight minutes from time Burgess rose acrobatically with an overhead kick from eight yards.
Just two minutes later the Tigers' new signing Ryan France rounded offan excellent home debut when he slid in from six yards to make it Hull's biggest win at their new stadium.
But in added time there was just enough time for Stuart Green to float in a superb free-kick to make it six of the best for City.