Paul Scott's header put the Shakers 1-0 up on the stroke of half-time but Stewart Drummond struck eight minutes from time to grab a share of the points.
It was an extremely scrappy first half, with neither team seemingly willing or able to play any kind of possession football.
Despite the lack of goal scoring opportunities, Shrewsbury always posed a threat at set pieces thanks to their giant centre halves.
Darran Kempson was first to get an effort on target six minutes in, his header from Dave Hunt's corner comfortably saved by keeper Jim Provett, before Kelvin Langmead headed just over the bar from another Hunt corner.
The only real spark of the contest came from Nicky Adams, the lively Bury midfielder almost finishing a move he had started himself, firing narrowly wide of the post.
But just as it seemed the teams would be going in at the break all-square, the Shakers struck in first half stoppage time.
Shrewsbury failed to deal with a left-wing corner and although Glyn Garner saved well from Glynn Hurst in the ensuing panic, Scott's rebound header just crept over the line.
The visitors could have equalised almost straight away, but Drummond's diving header went wide of the home goal.
That strike buoyed Bury and they had a string of chances to extend their lead after the break. Adams shot wide and Hurst too came close but the best chance fell to Andy Mangan, who blazed over the bar from all of five yards.
But Drummond made them pay, firing in off a post to cap a long spell of late Shrewsbury pressure.