George Boyd, Craig Mackail-Smith and Aaron McLean all scored for the visitors during a dominant display with Dagenham scoring two late consolation goals.
Posh started brightly with Dean Keates firing inches wide from the edge of the box in the first minute.
Midfielder Jamie Day tried his luck a minute later when he thundered an audacious shot narrowly wide from 30 yards.
Dagenham keeper Tony Roberts kept the scores level in the 15th minute when he spread himself to block at the feet of Mackail-Smith when he was through on goal.
Dagenham full-back Scott Griffiths hammered a bullet-strike through a crowd of players in the 25th minute which had Peterborough keeper Joe Lewis scrambling.
Roberts came to the rescue for his side again in the 30th minute when he blocked another Mackail-Smith effort from point-blank range.
The former Wales goalkeeper pulled off a spectacular reflex save in the 50th minute to turn a powerful Keates volley over the bar.
Keates came close again three minutes later when he saw his close range shot deflected wide of goal.
The visitors finally broke the deadlock in the 57th minute when Boyd fired calmly past Roberts from the edge of the box to finish off a clever Peterborough move.
Dagenham midfielder David Rainford had the chance to level the scores in the 68th minute but saw his 15-yard strike rebound off a Peterborough defender.
Mackail-Smith doubled his side's lead in the 72nd minute when he side-footed into the net from six yards after running onto a McLean cross.
The former Daggers striker should have made it three a minute later when he shot past Roberts only to see full-back Griffiths clear the ball off the line.
The home side were handed a lifeline in the 81st minute when sub Ryan Hall was felled by Craig Morgan in the Peterborough box with Rainford stepping up to fire home from the spot.
The come-back was shortlived with McLean making it three when he beat the Dagenham offside trap in the 84th minute and curled his shot past Roberts from ten yards.
Hall scored a second for Daggers deep in stoppage time but by then the match was won.