The better side in the first half, Rangers went a goal down when goalkeeper Gary O'Connor sliced a clearance to John Dillon, who made no mistake.
Rangers had a strong penalty claim rejected when Darren Smith was brought down.
In the second half Rangers attacked without creating any threat and their shooting was woeful. The Sons went two up after 58 minutes when John Wight launched a long free-kick from the edge of his own area. Eddie Annand jumped above two defenders to flick on to an unmarked Andrew Rodgers, who netted.
Nine minutes later the experienced Annand was left completely unmarked as Chris Boyle played the ball through to him and he rolled the ball under the despairing Gary O'Connor.
The Rangers goalkeeper saved with his feet from Rodgers as the Dumbarton star man broke through again.
This was Berwick's third successive defeat and manager Sandy Clark is facing an increasingly tough task.