The gusting wind made it difficult for both sides, but it was the visitors who looked the slicker side and they took a deserved lead midway through the first half.
Steven Rennie fired a low cross into the box and from 12 yards Barry Sellars' clever flick sent the ball curling over Stephen Grindlay into the corner of the net.
Dumbarton would have been content to reach the break at 0-1 as they would have the elements behind them in the second half, but just before they interval they gifted Arbroath a second.
David Craig and Grindlay needlessly got in a mess on the edge of the penalty area, leaving Willie Martin the easiest of task to knock the loose ball home.
Ryan Borris had a good chance to get the home side back into it in the 42nd minute, but Mark Peat made his only serious save of the game to turn away the winger's shot.
As the game progressed it remained Arbroath who were always the more dangerous, Grindlay touching over a Sellars header and substitute Jon Voigt hitting the bar after a great solo run by Marc McCulloch.