The home side dominated from the off and, despite losing striker John Gemmell to injury, really took command of the game midway through the opening half when summer signing David Bagan fired a curling 20-yarder high into the net for his third goal in as many games.
Almost immediately they nearly made it two when full-back Craig Brittain ended a solo shot with a fierce drive which rattled the crossbar.
After the break Shire began to play a bit but despite seeing plenty of the ball the failed to trouble Stephen Grindlay in the Sons' goal.
Dumbarton introduced ex-Hearts man Jose Quitongo as a trialist shortly after the hour-mark and it was the veteran striker who sealed the points when he fired in off a post from 12 yards after David McNaught had dispossessed dithering Steven Learmonth inside the penalty area.
Alan Ward had a great opportunity to snatch a consolation goal right at the death but despite being clean through he could only shoot against the advancing Grindlay.