Kenny Miller, Lee Wallace and Kris Boyd grabbed the goals for the visitors who could even afford to miss a first half penalty.
The win leaves Rangers six points behind the Jambos who face Hibs in the Edinburgh derby on Sunday.
After Nicky Law had gone close in the ninth minute, Rangers missed a great chance to break the deadlock from the spot on 24.
David van Zanten fouled Wallace in the box only for Lee McCulloch to have his spot kick saved by Daniel Rogers.
However, two minutes later the visitors did take the lead through Miller who latched on to Steven Smith’s cross to find the back of the net with a rising shot.
Boyd almost added a second with a 39th minute header while Garry Fleming and Mark Gilhaney went closest for Dumbarton before the break.
Boyd also produced the first real effort of the second half, forcing Rogers into a good save on 49.
At the other end Mitchel Megginson went close from outside the box but the hosts were powerless to prevent Rangers from doubling their advantage on the hour.
Miller laid the ball to Wallace who located the bottom right-hand corner of the net from 12 yards.
And Boyd made certain of three points 18 minutes from time when he headed home from Smith’s cross.
Rangers could have added more during the closing quarter of an hour as they continue to perform well away from Ibrox having not suffered a league defeat on the road since October 2012.