An early own goal had put the visiting Salop side ahead, before Barnsley forward Sam Winnall equalised before half-time.
Clark struck a dramatic added time winner to spark mad scenes in the away end.
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Barnsley 1 Shrewsbury 2 - Fan pictures
Published 6th Sep 2015, 10:01 GMT
Check out our picture gallery of supporters attending Shrewsbury Town's first League One win of the season at Barnsley yesterday.