The visitors, who conceded five at Charlton last week, let in more than three goals for the sixth time this season as Saints celebrated their 125th birthday in fine style.
Lee Barnard fired them ahead after 30 minutes, taking Rickie Lambert’s pass in his stride before making ground to lash his shot past Joe Lewis’ left hand.
Southampton effectively sealed the points with two goals in the first five minutes of the second half. First, defender Jose Fonte rose high at the far post to head home Ryan Dickson’s cross within 30 seconds of the restart.
Within two minutes Saints took command with a superbly crafted goal which saw Alex Chamberlain win the ball on the halfway line and feed Dean Hammond, who picked out Richard Chaplow to volley home his first goal for the club from eight yards.
Peterborough pulled a goal back through Aaron McLean, who broke free to lift the ball over Saints keeper Kelvin Davis. But any hopes of a fightback were dashed when Brazilian striker Guly Do Prado restored the three-goal cushion by escaping some poor Peterborough marking to glance home a header from Lee Holmes’ free-kick.