The visitors failed to muster an effort on target for 80 minutes until substitute Tom Bradshaw finally tested goalkeeper Sam Slocombe from long range.
Despite dominating most of the possession, struggling Scunthorpe could not make it count, leaving them still with only one home win all season.
Their only real effort of the first half came when striker Nathan Ellington, making his full home debut on loan from Ipswich, tested keeper Chris Weale with a free-kick.
Scunthorpe threatened more often in the second half with Jimmy Ryan and substitute Andy Barcham both testing Weale and striker Karl Hawley fired just inches wide from the edge of the box.
The Iron threw men forward in the closing stages and Ryan nearly snatched them the three points with a rasping drive that whistled just wide.
Shrewsbury then came even closer to sneaking a winner in stoppage time when a brilliant effort from Jon Taylor looked destined for the top corner until the ball was tipped away at full stretch by Slocombe.