Grimsby recorded their first home victory in the league since March thanks to Adam Proudlock's winner.
He was on target after 53 minutes, volleying in Nick Hegarty's cross to give manager Mike Newell his first success at Blundell Park.
Liam Trotter should have given the Mariners the lead earlier, but Shrews' keeper Matt Jilks saved his effort.
Shrewsbury should have levelled just after Proudlock's goal, but Jamie White shot wide after racing clear.
Booked: Proudlock.
Goals: Proudlock 53.
Shrewsbury: Gilks, Darren Moss, Coughlan, Langmead, Cansdell-Sherriff, Davies, Murray, McIntyre (Hunt 76), Ashton (Hibbert 66), White, Holt. Subs Not Used: Daniels, Herd, Leslie.
Booked: Langmead, Hunt.
Att: 3,283
Ref: Steve Bratt (W Midlands).
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