Stuart Drummond earned Shrewsbury a share of the points with a goal eight minutes from time at Bury.
The home side went ahead on the stroke of half-time with a Paul Scott header which crept over the line after a corner was not properly cleared.
Bury had a string of chances to add to their lead, Andy Mangan blazing the best one over the bar from five yards.
The Shrews threw everything at Bury in search of an equaliser which they found when Drummond fired in off the post.