The hosts moved into a 51st-minute lead when Jon McShane struck only for Craig Johnstone to equalise for the Fifers.
However, Mark Gilhaney's cool finish on 61 minutes and McShane's second of the day 13 minutes from the end confirmed Dumbarton as winners.
Dumbarton: Grindlay, Chisholm, McNiff, Gordon, Nugent, Creaney, Gilhaney, Geggan, McShane (Campbell 90), McStay, Walker (Jordan White 80). Subs Not Used: Michael White, McLeish, Tony Wallace.
Booked: McStay, Jordan White.
Goals: Geggan 39, McShane 51, Gilhaney 68, McShane 77.
East Fife: Michael Brown, Smart, McCulloch, Ovenstone, McGowan, Muir, Linn, Park, Hislop (Wallace 46), Young, Johnstone. Subs Not Used: Lyness, Durie, Fagan, Cargill.
Goals: Linn 27, Johnstone 61.
Ref: Stevie O'Reilly
Source: BBC Sport