Ryan Cresswell nodded the Shrimpers in front after 17 minutes when he charged in to the penalty area and headed a right wing cross from Kevan Hurst in to the back of the net via the inside of the left post.
Paul Sturrock's side then doubled that lead in the 62nd minute when a sliced clearance from Dagenham defender Luke Wilkinson enabled Britt Assombalonga to fire the ball in to a gaping goal from six yards.
Dagenham made a triple substitution immediately after the second goal with Sam Williams, Dominic Green and Dwight Gayle all coming on.
And they helped Daggers get on top in the closing stages.
Williams and Green were both denied by fine saves from Southend goalkeeper Paul Smith in quick succession before Gayle headed against the underside of the crossbar from 12 yards.