Ball opened the scoring after only three minutes when former Daggers forward Craig Mackail-Smith laid the ball off to his strike partner who slotted home past Tony Roberts in the keeper's 500th game for the home side.
The former Manchester City striker, making only his third start of the season, then doubled the lead after eight minutes when the ball fell kindly to him in the box and he made no mistake with the finish.
Oliver Lee had missed a chance in the third minute for the Daggers as he fired his shot across goal and wide.
Dagenham enjoyed plenty of possession in the second half but failed to penetrate a sturdy Peterborough defence.
Mackail-Smith found the side-netting in a rare Posh chance after the break, before firing the best opportunity of the second half just wide after good play from Ball and George Boyd.