The hosts were under the cosh in the early exchanges as Alister Crawford tested home goalkeeper Stephen Grindlay before Gary Fisher hit the bar.
Hamilton's efforts bore fruit in spectacular fashion after 23 minutes when Crawford attempted a lob from 30 yards out which Grindlay could only watch sail into the net.
The Accies were two goals to the good just before the break with Michael Devlin finding space outside the box to curl home, before Jonathon Routledge hit the woodwork.
Chris Turner gave Dumbarton hope when he met Mark Lamont's cross from the left to head in just before the hour mark, but substitute Grant Gillespie responded with a chipped finish to wrap up the contest 15 minutes from time.
The hosts were then reduced to 10 men when Chris Turner was sent off for a second yellow card.