The club's record signing could hardly miss from four yards after being picked out by a 57th minute cut-back from Nathaniel Mendez-Laing as Posh saw off League Two opposition for the second time in four days - this success following hot on the heels of an FA Cup first-round triumph over Exeter.
The breakthrough arrived seconds after the visitors had spurned a glorious chance of their own.
The stooping Abu Ogogo contrived to head a terrific Gavin Hoyte cross over the bar from close range.
The teams had earlier traded good opportunities in the early stages.
Daggers frontman Chris Dickson saw a shot blocked by home skipper Michael Bostwick after springing the offside trap before Posh loanee Hogan Ephraim was denied a first goal for the club by a fine goal-line clearance from defender Brian Saah.
Daggers keeper Chris Lewington palmed away a long-range Assombalonga blast before Grant McCann crashed a free-kick against the bar in the final action of the first half.