Indeed it was Hibbert who found himself in space in the box after only 15 seconds, but shot tamely at stopper Andy Warrington.
In a bitty start to proceedings, the Millers most likely goal threat came from the recalled Kevin Ellison, booed by home fans with each touch after his time with Chester City.
But it was Fairhurst, on loan from Donny Rovers, that was next to fire in a shot at Warrington's goal but it whistled five yards wide of the upright.
Almost immediately though Ellison carved out a chance down the left but as he cut into the box, his vicious shot deflected for a corner. Ian Sharps rose highest from the resulting flag kick but his header drifted wide of Button's post.
On the half hour a foul on Graham Coughlan by Ian Sharps saw Warrington at full stretch to save Hibbert's spot kick, and Tom Pope produced a heroic challenge to prevent the rebound as it went goalwards.
But the Shrews took the lead minutes later as Fairhurst's drilled shot from outside the box flashed past the diving Warrington who appeared to pick up sight of the ball late.
After the break alot of neat ball play in midfield by the Millers failed to turn into direct chances, with Adam Rundle's shot clipping the top of the crossbar and Ellison striking the best effort over the bar from a free kick after a foul on Pope on the hour.
Ellison again went close with 12 minutes left before he was substituted, but his driven left foot effort went over.
And the Shrews sealed the three points with just two minutes left as Devitt picked up the ball on the angle and his low drive deflected off Nick Fenton and squirmed past Warrington.