This often untidy encounter was ultimately decided with a quarter of an hour remaining when Grant Holt netted his 20th goal of the campaign to secure a vital win over the Gigg Lane side - who were forced to play with ten men from the 38th minute after central defender Efetobore Sodje was ordered off for using an elbow on Shrewsbury striker Michael Symes.
Despite being a man short Bury were still in the match until Holt struck so decisively. This victory lifts Shrewsbury back into the play-off frame and at the same time they leapfrog Bury into fifth place.
Following their 2-1 Boxing Day defeat at Rochdale, which had seen Shrewsbury slip from the play-off places, Town boss Paul Simpson rang the changes, recalling striker Michael Symes and young winger Chris Humphrey.
But neither they or any other forward on view was able to make much headway in the early stages, but by the half hour mark things began to warm up and twice Shrews' keeper Luke Daniels had to thwart Michael Jones, while at the other end Bury goalkeeper Wayne Brown did well to hold a far post header from Shrewsbury's Kelvin Langmead.
But seven minutes before the break, the game took a decisive turn when Sodje was sent off by referee Mark Haywood for an apparent use of the elbow on Symes and as a result Bury manager Alan Knill withdrew striker Andy Morrell and sent on defender Ryan Creswell.
The visitors made it to half-time without any undue alarms and withstood a number of spells of second half Shrewsbury pressure, even managing to break away for Elliott Bennett to fire into the side-netting.
14 minutes from time, however, Bury finally cracked when Shrewsbury skipper Ben Davies crossed dangerously into the box, Holt was on hand to power home a header from eight yards.