The rot started after seven minutes when Chris Neal parried a shot from Mark Duffy only for Sean Holden to head into his own net.
Shrewsbury lost skipper Ian Sharps with a head injury after 25 minutes and three minutes later James Spencer was first to a loose ball to toe poke home in a goalmouth scramble.
After 48 minutes Mat Sadler tripped Duffy and Laurence Wilson scored from the spot.
Spencer saw red for violent conduct but despite Shane Cansdell-Sherriff volleying home following a corner in the 67th minute, Morecambe held on thanks to a string of fine saves by Barry Roche.
Source: PA
Source: PA