The success means that Accrington secure their fifth consecutive victory as they continue their surge towards the upper reaches of the Conference table.
Accrington had the better of a tight first half with Gary Roberts in particular causing problems for the home defence. The winger had a good chance to open the scoring with an attempted lob that beat Dagenham keeper Tony Roberts, only for the ball to drop over the crossbar.
The visitors thought they had taken the lead just after the half-hour mark as Paul Mullin tapped in a low cross from Roberts. Their celebrations were cut short however as Mullin was adjudged to have scored from an offside position.
Dagenham's best chance in the first half came from their striker Chris Moore. Moore unleashed a powerful left-footed shot that brought a good save from goalkeeper Darren Randolph.
All the goals were scored during the second period and it was Accrington Stanley who took the lead four minutes after the break. Roberts saw his left-footed shot blocked, but the ball fell kindly to David Brown who rolled the ball into an unguarded net.
Accrington doubled their advantage ten minutes later. The referee decided that Glen Southam had tripped Anthony Barry and awarded a penalty. Ian Craney stepped up and scored in the bottom right corner.
The Daggers got themselves back into the game as Tresor Kandol scored from close range after latching on to a Craig Mackail-Smith cross.
John Still's men pushed forward for an equaliser in the latter stages and both Moore and Paul Benson went close, but Accrington held on.