The lively Jon Taylor's 81st-minute cross from the right took a deflection and goalkeeper Bartosz Bialkowski was left red faced as he fumbled the ball into his own net.
The Shrews had gone in front in the 19th minute with a neatly-taken goal from County old boy Luke Rodgers. He reacted quickest to lift the ball over Bialkowski after Marvin Morgan nodded down a Darren Jones free-kick.
County were quickly level with a goal claimed by Lee Hughes, although the final touch to Alan Judge's corner seemed to come from home defender Cameron Gayle.
Shrewsbury then enjoyed a good spell with Aaron Wildig heading narrowly wide before a Matt Richards thunderbolt was superbly saved by Bialkowski.
County moved ahead on the stroke of half-time as Judge raced almost the length of the field to force a save from Chris Weale with Jamal Campbell-Ryce stabbing in the rebound.
Judge almost increased his side's lead in the second half but was twice denied by Weale before Shrewsbury, beaten just once in their last seven games, left it late to claim a point.
