Securing their sixth win in eight games, the Rams bore no resemblance to the side that lost their first 12 matches in the Championship and looked certainties for the drop.
James Craven scored the first of their six tries and Pat Walker, having recently re-discovered his confidence, added the first of six goals.
The Rams went 12-0 ahead when Walker scampered over in support of a pile-driving burst by Bryn Powell.
Walker converted that, and the 39th-minute try by Luke Stenchion, when the prop charged over between the sticks.
Dewsbury went 24-0 up when Rob Spicer spotted a gap and strode through to score as Barrow backed off. Walker added his fourth goal and converted Dewsbury's fifth try when Powell finished off a fine move that created an overlap in the corner.
Barrow scored a consolation try via James Coyle as Jamie Rooney added the goal.
A fightback seemed unlikely and Dewsbury nipped any thoughts in the bud when Brambani kicked to the corner for Powell to win a race to the line for his second touchdown. Brambani turned the screw with some deft half-back play before he added a 35-metre drop-goal.
Dewsbury Rams: Craven, Powell, Bretherton, Turner, Buchanan, Walker, Brambani, Hirst, Blake, England, Spicer, Lockwood, Barber. Substitutes: Stenchion, Robinson, Tonks, Emmett.
Barrow Raiders: Broadbent, Ballard, Blackwood, Harrison, Bauer, Coyle, Rooney, Bracek, Carlile, McDermott. Ostler, Catic, Luisi. Substitutes: Mossop, Noone, Butler, Young.
Referee: G Hewer (Whitehaven).