Goals early in each half from Curtis Main and Harry Chapman helped Shrewsbury condemn Burton to a second successive 2-1 defeat easing their own relegation fears in the process.
Shrewsbury weathered early Burton pressure to grab a seventh-minute lead. A free-kick was played to Nathanael Ogbeta on the left and his deflected cross bounced awkwardly inside the penalty area with Main claiming a crucial touch to glance it beyond Ben Garratt as Tom Hamer frantically tried to clear off the line.
Michael Bostwick headed into the side netting on the stroke of half-time as Albion struggled to break down an obdurate Shrews defence.
The second half followed the same pattern as the first with Albion coming out strong and being caught cold when Ogbeta crossed for Chapman to volley home.
On the hour Albion halved their arrears, Sean Clare driving into the box to drill a rising drive beyond Harry Burgoyne. Despite a late press the visitors held on to take the points.