Steven Learmonth was deemed to have pulled down Andy Geggan and, although the referee initially awarded a free-kick on the edge of the area, his assistant persuaded him that the offence had taken place inside the penalty box.
That didn't worry Stephen Dobbie who calmly stepped up to give his side the lead from 12 yards.
Dumbarton's Craig Brittain blocked an absolute pile-driver from Paul Stewart before Shire should have equalised after 41 minutes.
Stephen Adam's accurate free-kick eluded the visitors defence only for Steven Dymock to blaze over the top of an open goal.
A minute after the restart Anton Nugent kept his side in the match with a save from Dobbie but an effort from home player Adam gifted the visitors a second goal.
The midfielder tried to be too clever on the edge of his own box and was caught in possession by David Bagan and, as he broke into the box, there was not a defender in sight to stop him from firing a shot behind the unprotected Nugent.
Shire kept going to the bitter end but as they had little to offer up front there was never any danger of Dumbarton losing a goal.