Second half strikes from Mark Russell and Kudus Oyenuga emphasised their superiority against a Sons side who remain just above the danger zone.
In a drab opening, any attacking intent came from the visitors who forged the first chance on 22 minutes when Andy Murdoch’s low shot forced a diving save from Alan Martin.
They threatened again when Gary Oliver curled an effort narrowly wide.
But Dumbarton almost opened the scoring with their first genuine attempt on the stroke of half-time, Sam Stanton firing just over.
Sons suffered a double blow on the restart when Mark Docherty and Frazer Wright were forced off through injury.
Morton almost cashed-in while their hosts re-organised, Oliver and Russell forcing diving saves from Martin in quick succession.
But the visitors were quickly back on the offensive and took the lead when Russell controlled a loose ball on the edge of the box and sent a left-foot shot low into the corner.
And Morton put the issue beyond doubt when home keeper Martin was left stranded as Oliver fed Oyenuga for a tap-in.