In-form Morecambe took their unbeaten run to 12 games after a dull stalemate.
Shrews top scorer Grant Holt missed the best chance of the game on the stroke of half-time when he broke clear but scuffed his shot.
Shrewsbury had two penalty shouts when sub Richard Walker was sandwiched by David Artell and John Bentley, who later bundled Holt off the ball.
But Morecambe ended the game on top, with former Shrews players Artell and Stewart Drummond impressive.
Shrewsbury: Daniels, Darren Moss, Langmead, Coughlan, Ashton, Humphrey, Murray (Leslie 58), Dunfield, Davies (Worrall 76), Holt, Ashikodi (Walker 58). Subs Not Used: Chadwick, Cansdell-Sherriff.
Booked: Ashikodi, Darren Moss.
Morecambe: Roche, Artell, Bentley, Adams, Yates, Curtis, Hunter, Drummond, Wainwright, Twiss, Howe. Subs Not Used: Edge, O'Carroll, McLachlan, Duffy, McStay.
Booked: Hunter, Howe.
Att: 5,426
Ref: Oliver Langford (W Midlands).
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