Rovers fell to defeat in Shropshire on a frustrating afternoon which had seen them force home goalkeeper Max O’Leary into a number of good saves and rattle the woodwork before being hit by a late goal.
O’Leary had to scramble to turn away second-half efforts from Ben Whiteman, Cameron John and Madger Gomes, while Jacob Ramsey also saw an effort come crashing back off a post.
But Dave Edwards headed home from Callum Lang’s cross after 78 minutes to ensure Sam Ricketts’ Shrews claimed all three points.