The striker netted twice in the first period to send the Shrimpers on their way before Ryan Cresswell added a third in the second half.
Paul Sturrock's side played 82 minutes with an extra man after Daggers defender Luke Wilkinson was dismissed for a professional foul on Gavin Tomlin.
Following that red card, Southend went in front after 18 minutes when Sean Clohessy crossed from the right and Assombalonga headed the ball in to the top-right hand corner of the net.
The on-loan Watford youngster doubled his tally just before the break when he bundled home inside the six-yard box after Kevan Hurst's low shot had been parried out by Daggers keeper Chris Lewington.
The visitors got back in to the game on the stroke of half-time when Dwight Gayle's right-wing cross squirmed in, however, the Shrimpers made sure of their win 20 minutes from time when Cresswell volleyed in from 14 yards.