Jake Leberl was also on target for the home side, with Steve Daly netting for the Sandgrounders. However the Lancaster side's inability to defend from set-pieces cost them dearly.
Dagenham started at a frenetic pace and were unlucky not to take the lead on 11 minutes when Chris Moore rose unchallenged to head a Glen Southam corner past keeper Steve Dickinson, but sadly for the Daggers, only on to the bar.
Dickinson was in action again on 17 minutes, tipping Southam's looping cross over his bar and only Dominic Krief's goal-line clearance midway through the first half prevented Southport from going one behind.
The Daggers pressure was relentless and Dickinson had to be alert once again, tipping Leberl's 25-yard drive on 30 minutes, but a minute later, the home side took the lead.
Paul Bruce's corner was acrobatically put in by Mackail-Smith as the Southport defence looked on. The lead however lasted only a few seconds.
Straight from the re-start, Southport's Terry Ferns crossed from the left, and Daly stole in in-between central defenders Shane Blackett and Anwar Uddin to power his header past Tony Roberts for a 1-1 scoreline at the break.
Within six minutes of the re-start, the Essex side restored their lead. Bruce swung in a corner which confused the Southport defence as first Uddin headed goalwards, the loose ball ending up in Leberl's path, who slotted home from close in, once again the Southport defence were unable to defend a corner.
Southport's gutsy determined style deserved something from the game, but in time added on, Mackail-Smith's instinctive shot from substitute Paul Benson's cross further punished the visitors.
The Essex side played some neat football and will feel this an excellent start to their campaign.