The clash between two sides known for their attractive style lived up the billing, with play flowing from end to end in a pulsating encounter at St Mary's.
Swansea dominated proceedings after Lallana's first-half strike, only for substitute Rodriguez to make the most of slack defending to secure a 2-0 win for Mauricio Pochettino's side.
The result was harsh on Michael Laudrup's team, who showed no signs of a hangover from Thursday's Europa League clash against St Gallen as they pressed from the outset.
After Lallana latched onto a neat ball from Steven Davis to put Saints ahead, Artur Boruc was forced into fine saves to stop Michu and Wilfried Bony levelling.
Nathan Dyer also hit the inside of the post as half-time approached, with Swansea continuing in the ascendancy after the break.
However, Southampton kept the Welsh side at bay to earn a fifth clean sheet of the term, with Rodriguez slotting home seven minutes from time after seeing a Victor Wanyama goal dubiously ruled out.
It was harsh scoreline on a Swansea side that made five changes from the win over St Gallen.
One of those to come in was Saints academy graduate Dyer, who burst down the right flank early on only to be blocked off by Dejan Lovren.
Jonjo Shelvey tested Boruc soon after as Swansea controlled the early tempo, but Saints soon settled into their stride.
Source: PA
Source: PA