On-loan Aberdeen striker Mitchell Megginson doubled the visitors' advantage when he slotted home Ian Nimmo's corner.
The home side came close to pulling a goal back, but Derek Carcary's header was straight at the Arbroath keeper.
Dumbarton: White, Clark (Carcary 53), McNiff, Chisholm, Dunlop, Geggan, Chaplain (Hunter 84), McStay, Murray, Winters, Wyness. Subs Not Used: Vonacek, Cook, O'Donoghue.
Booked: Dunlop, Geggan.
Arbroath: Hill, Doris, Moyes, Rattray, McCulloch, Ross (McLean 75), Redman, Mclaughlin, Booth, Megginson (McIlravey 84), Nimmo (Gibson 64). Subs Not Used: Morrison, McMullan.
Booked: Redman, Mclaughlin.
Goals: Redman 39, Megginson 49.
Ref: S Finnie