Billy Paynter slammed home the spot-kick after Shrews skipper Matt Richards had brought down David Cotterill, but Rovers rarely tested visiting keeper Chris Weale after that.
Rovers had most of the first-half play and produced some decent football but lacked an end product, although David Syers was unlucky to see a spectacular strike disallowed for offside.
Shrewsbury missed a series of good chances when they tried to battle back with Marvin Morgan heading wide from John Taylor's cross with the goal at his mercy.
Home keeper Gary Woods did well to parry a shot from Morgan into the side netting in the 63rd minute and Paul Parry headed another chance wide five minutes later.
The closest that Shrewsbury came to an equaliser came soon after that when Rovers skipper Tommy Spurr hit the ball towards his own goal in an attempt to clear a shot causing his startled keeper Woods to make an instinctive save.