Despite being the better side in the first half, they went in a goal behind but persevered with good football after the interval and got their just reward at the end of the day.
The visitors struck early when Steven Mackay headed in an Alan Dempsie corner in the sixth minute. Shire should have had an equaliser when Alan Ward head-flicked an Andrew Brand cross into the path of Derek Ure whose weak finish from four yards allowed keeper Keiron Renton to save the day at the expense of a corner.
The keeper later hurt his back turning a Paul Stewart strike over the crossbar and lady luck was still against Shire when a Ward shot rebounded from the crossbar with Renton well beaten.
The visitors went down to 10 men after 41 minutes when Adam Nelson injured himself when committing a serious foul and the referee flashed the card at him as he left the field on a stretcher.
Shire's two-goal fight-back began when substitute Steven Dymock headed the equaliser from Ure's fine cross before Paul Tweedie hit the winner from a Ward pass. Elgin tried to stage a late fight back but the Shire defence held out comfortably and the home side even had chances to put the issue beyond doubt.