Derek Ure's goal after four minutes turned out to be the winner with a chance that came out of nothing.
The ball seemed to bounce away from two Rovers defenders conveniently into his path, allowing him to run into the penalty area before beating Gary McGlynn with a low left-foot shot.
Chances were few and far between as both teams lacked a cutting edge in front of goal, but Rovers should have equalised in the 39th minute. Stephen Donachy's low cross was met by Scott Chaplain six yards out, but somehow Derek Jackson threw his body in the way to keep Shire in front.
The same thing happened at the other end in the second half and this time it was McGlynn's turn to deny Ure a second goal. Scott Livingstone then wasted the opportunity to make the game safe for Shire by hammering the rebound over the bar.
Rovers looked the more likely side towards the end, and substitute Stephen Reid saw his shot deflected on to the bar before the home defence scrambled the ball to safety.
A minute later Steven Dymock had a chance to finish the game but lost his nerve and sent a poor finish straight at McGlynn.