Stuart Elliott had a chance after making a driving run but shot wide.
Kidderminster were then denied when Alan Fettis tipped Sam Shilton's shot over, and Bo Henriksen had a goal disallowed for offside 10 minutes before half time.
Burgess then rubbed salt into the Harriers' wounds by doubling the lead. When Dion Scott was unable to clear the ball, the 6'3" striker took a stab at the ball and found the back of the net.
Jon Walters looked to get one before half time but saw his curled shot saved by Stuart Brock, while Elliott headed wide.
In the second half, Walters, Melton and Elliott were all wasteful with chances, and the visitors pulled one back with an hour gone. Henriksen challenged Justin Whittle for the ball on the sideline, and with no free kick given he crossed into the box. Fettis leapt to punch the ball clear, but only as far as Sean Parrish who burried the shot.
Kidderminster pressed for an equaliser, but 10 minutes from time City's nerves were calmed as Walters raced onto Elliott's ball down the channel and slotted home first time past the approaching goalkeeper.
Then with two minutes to go Ben Burgess sealed the win - and his hat-trick - by looping a header over Stuart Brock.
In frustration at seeing their chances of reaching the play-offs go, Craig Hinton brought down substitute Daniel Webb but escaped with a yellow card.
14,544 were at the Kingston Communications Stadium for the last time this season to see City win 4-1 - the biggest scoreline so far at the stadium.
City line-up (4-4-2): Fettis; Otsemobor, Whittle, Joseph (Burton 64), Delaney; Regan, Melton, Keates, Elliott (Webb 87); Walters (Russell 83), Burgess.
Un-used subs: Musselwhite, Reeves.