After a dull opening ten minutes, the home side were the first to register a shot on goal when a Euan Donaldson cross found its way to Alan Brazil, but he curled his shot wide.
Five minutes later Dumbarton created their only chance of the half when a James Allan run was stopped by Donaldson and Barry Donald fired the loose ball just over.
After that scare, Arbroath took control of the game. A Donaldson goal direct from a corner was ruled out for a push by Chris McLeod on Dumbarton keeper Stephen Grindlay.
However, shortly afterwards Arbroath took the lead when a fantastic pass by Donaldson sent Gavin Swankie through on goal and he squeezed the ball past Grindlay at his near post.
It took a disappointing Dumbarton side 63 minutes to finally get behind the Arbroath defence when an Eddie Annand flick-on sent Allan in on goal, but Neil Inglis did well to block his effort for a corner.
Arbroath once again responded well with a John McGlashan 30-yard shot striking the bar before Greig Henslee scored the second goal, slotting home from a weak Mark Dempsie clearance.
Annand pulled a goal back later on, but once he was dismissed for two bookings the game was over as a contest.