The goals from Wilding on seven minutes and Rodgers on the quarter hour mark gave Harriers a mountain to climb.
They went on to create their fair share of chances but failed to really seriously test visiting keeper Cartwright.
Inbetween the goals Smith put over a good cross from the right but Melligan rose to head wastefully off target.
It was Bishop who had the next Harriers chance on 18 minutes from a Melligan pull-back from the right, created by Williams incisive but he scuffed a shot wide on the turn. John Melligan
Shrewsbury had to make a substitution on 22 minutes with Tolley off injured and Jagielka taking his place.
But the visitors could have gone further ahead on 29 minutes when substitute Jagielka flicked the ball across for Rodgers who directed a looping first-time volley over the bar.
Keeper Cartwright created hard work for himself four minutes later, scrambling Bishop's long range effort wide awkwardly when the ball appeared to be heading in that direction anyway.
Harriers midfielder Melligan was booked for dissent on 36 minutes and then Bishop missed a great chance soon after.
The forward was found by Flynn's flick from a Williams pass he opted to take his opportunity first time and slipped the ball disappointingly wide.
Seconds later he directed a low 25-yarder just wide of Cartwright's upright.
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