The Shrews seemed shocked by the sacking on Friday of boss Paul Simpson, started slowly at the Prostar Stadium, and were two goals down to the Shrimps after 16 minutes.
The outstanding Mark Duffy robbed Shane Cansdell-Sherriff before shooting into the far corner, and former Shrew David Artell was unmarked when he headed in Craig Stanley's free-kick.
The arrival of teenage substitute Tom Bradshaw turned the game in the 33rd minute. His first touch sent Benjamin van den Broek clear to score and then he hit the equaliser from 15 yards after 48 minutes.
But Stanley's free-kick was headed home by Artell once more after 62 minutes and the visitors had a let-off in stoppage time when Kevin McIntyre hit the crossbar with a penalty and Barry Roche saved brilliantly as Terry Dunfield tried to force in the rebound.