The Grizzlies dealt with the miserable conditions better than the home side, and their pack had the edge in the set pieces.
Southern lost a lot of lineout ball in the first 40 minutes and their scrum was back pedalling.
The first points actually came from a tighthead.
Southern was shunted off their ball and first five Finn Strawbridge snapped off a pinpoint kick-pass to winger Vilimone Bainibure, who just had to catch it, run a few metres and dive over.
Southern responded with a couple of penalties from the boot of Mackenzie Palmer.
Green Island lost a player to the bin either side of the half.
But it was the two yellow cards which Southern picked up midway through the second stanza which had a bigger impact on the game.
Replacement forward Corban Agar was binned for a high tackle and prop Tafa Tafa infringed at the ruck which cost his side a penalty try and he got a yellow card as well.
The visitors clinched the win with a try to impressive second five Riley Lucas with about 10 minutes remaining.
Loosies Ronan Dynes and Amos Roddick worked hard and Strawbridge controlled the game nicely and made some good decisions.Left winger Truman Cuff created a few half chances for Southern and experienced fullback Palmer did well at the back despite the challenging conditions.
In the other games, Dunedin was too strong for Alhambra-Union. The Sharks ran in 10 tries to win 66-0 at Kettle Park.
University out muscled Taieri at Peter Johnstone Park in a 27-10 victory.
And Kaikorai and Zingari-Richmond had to settle for a 20-20 draw at Bishopscourt.
Ben Miller was making his 100th appearance for the Demons and stretched his career tally for the side to 809 points.
