Harrriers were given an early warning on three minutes when Morgan inadvertently flicked on a Hilton long throw and Maylett pounced at the far post only for keeper Digby to block.
But the home side were ahead on eight minutes when Shilton's left-wing cross shot deceived everyone and rebounded in off the far post for his fifth goal of the season.
The wide man drove off target from 20-yards soon after before Swansea missed a good chance to equal on 17 minutes.
Maylett's run down the right ended in an accurate pull-back for top scorer Thomas but he blazed over the bar from 15-yards.
Swansea full-back Jenkins applied a vital clearance on 20 minutes as Brought waited to pounce from a Melligan cross.
However Swansea levelled on 22 minutes when a fierce 25-yard drive from Martinez rebounded off the body of keeper Digby for Johnrose to fire home from close range. Fraser Digby
Harriers were forced into a switch on 25 minutes with Stamps on for the injured Morgan for his first appearance since November after a groin operation.
He switched to left-back and boss Britton changed to a four man defence with Smith at right-back.
Harriers went back infront on 32 minutes with Smith's first goal of the season, a close range volley after his initial header from Shilton's corner had been blocked.
Three minutes later though Swansea were level with skipper Martinez curling home an excellent 20-yard free kick via the post.
The visitors nearly went infront for the first time but Digby did well to save Nugent's shot from an angle on 38 minutes.
Harrier midfielder Williams was booked a minute before the interval for a high challenge.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article