The Daggers, who lost 4-0 in the first meeting at St Mary's Stadium in November, set up with 10 men behind the ball and the first half mostly resembled a training game with their defence against the visitors' attack.
The breakthrough finally came in the 47th minute after a surging run from Alex Chamberlain, who chipped the ball into the path of the equally impressive Adam Lallana, who bicycle-kicked past home goalkeeper Tony Roberts.
An error from Daggers captain Will Antwi allowed Lee Barnard to play in Guilherme Do Prado in the 76th minute and the Saints midfielder calmly side-stepped Scott Doe and buried a shot into the bottom corner.
Daggers substitute Josh Scott pulled one back for the home side with a well-placed header and Gavin Tomlin hit the crossbar with a free-kick in the 89th minute as John Still's side piled on the pressure.
But Rickie Lambert lobbed Roberts in injury time to seal three points for the Saints.