An Alan Brazil brace and a Kevin McMullen strike secured the points for the Smokies after they produced a battling display at Forthbank.
Brazil opened the scoring after 36 minutes, firing beyond Myles Hogarth after beating Paul Nugent.
Eleven minutes after the restart McMullen doubled Arbroath's advantage.
Greg Miller fired in a cross and McMullen slotted home from close range.
Brazil completed the rout with his second four minutes later, dribbling round Hogarth and stroking the ball into an unguarded goal.
The result saw Arbroath leapfrog Berwick and move off the foot of the table.