Danny Foster's 25-yard shot forced a save out of recalled Southend goalkeeper Darryl Flahavan, but the hosts took the lead in the 11th minute.
Lewis Hunt brought the ball forward and picked out Dean Morgan on the left flank. His cross from the left byline was stabbed past veteran keeper Tony Roberts at his near post by Charlie MacDonald.
The Shrimpers nearly doubled their lead when Morgan's run beat the Daggers' offside trap. He squared to Hunt, but Roberts had the measure of his 15-yard shot.
The Daggers frequently used long balls to Jon Nurse, most of which came to nothing. But the forward, signed from Stevenage Borough, came up trumps with the equaliser on 32 minutes.
Ben Strevens' low cross found Nurse who slotted away his first goal for the Daggers from six yards.
The visitors were boosted by the goal and Nurse hit the side-netting before Strevens' header from close range was held by Flahavan.
Hunt's deflected shot was parried by Roberts as the second half got underway, before Flahavan denied Nurse at the other end.
But the Daggers took the lead in the 58th minute when Nurse slipped in the area and strike partner Strevens slammed the loose ball beyond Flahavan's dive.
The lead lasted just five minutes before the League One Blues were on terms. Matt Harrold teed up Morgan and he blasted the ball into the top left-hand corner from just outside the box.
Southend regained the lead in the 77th minute when Steve Hammell's corner from the left was only cleared as far as Simon Francis and he rifled the ball home through the crowded box from just outside the 18-yard box.
The Daggers were reduced to ten men when goalkeeper Roberts, who had come up for a corner, was sent off after appearing to butt Peter Clarke three minutes from time.
Southend made sure of the win in stoppage time with Nicky Bailey slotting home after reserve keeper Ed Thompson had parried Morgan's shot, and then Morgan scored from a yard out following MacDonald's cutback.