Jake Leberl opened Dagenham's account in the sixth minute when he met a corner from Paul Bruce with a close-range header on the back post.
Southport failed to create any real chances for themselves and were duly punished when Craig Mackail-Smith fired home as he ran unchallenged through the defence and scored from six yards out to double the advantage in the 17th minute.
Southport's only first-half chances fell to Neil Robinson, Steve Daly and Carl Baker, but nothing to concern or stretch Tony Roberts in the Daggers goal.
Southport finally ended their 630 minute goal drought on 49 minutes when Daly played the ball in from the right side of the box to the advancing Baker who sneaked the ball in low at the near post to give the home side the chance of a comeback.
Southport should have equalised five minutes later when Baker turned provider, pumping a ball in from the right wing but Nick Rogan's header flew over the Dagenham bar.
Dagenham were reduced to 10 men on 63 minutes when Leberl followed through on Rogan, with the referee adjudging the challenge worthy of a straight red card.
Southport tried to immediately seize on their advantage with Baker's free-kick being headed on to the crossbar by Mark Roberts and Rogan headed the rebound agonisingly over.
Southport themselves were reduced to 10 men when Daly was dismissed for his actions in an altercation just outside the Dagenham area.
However, Southport continued to search for the equaliser with Matty McGinn forcing a good save from Roberts with a shot from the edge of the box.
But despite Southport's late pressure, Dagenham held on to claim the points.