Goals from Richard Chaplow and Jos Hooiveld helped Saints - who have made their best start to a season in 55 years - into a 2-0 lead within 17 minutes.
Peterborough suffered a further setback when Lee Frecklington was dismissed for a second booking 10 minutes before half-time.
But, after goalkeeper Paul Jones kept them in the game, the visitors pulled a goal back with 14 minutes left through substitute Emile Sinclair but it was not enough to prevent them from going down to a third straight loss.
With second-placed West Ham being held to a goalless draw by bottom-of-the-table Bristol City, it meant Southampton stretched their lead at the top to five points.
Saints surged into a two-goal lead inside 17 minutes.
Chaplow opened the scoring in the 14th minute when he passed the ball into the bottom corner after a one-two with Guly Do Prado - his first goal in nine games.
Three minutes later the home side doubled their advantage. Rickie Lambert's free-kick found Do Prado and he in turn crossed for Hooiveld, on loan from Celtic, to convert from close range.
Peterborough, who have banged in 28 goals in 14 league games, came close to pulling a goal back but George Boyd's shot from 12 yards went wide.
Saints, free-scoring this season themselves, then nearly made it 3-0 but Jones punched away Lambert's 20-yard drive.
The night got even worse for Peterborough in the 35th minute when Frecklington - booked 15 minutes earlier - received his second caution for a foul on Morgan Schneiderlin.
Just before half-time, Schneiderlin drilled a 30-yard effort over the bar as Saints continued to dominate.
There was still time for Peterborough to produce another attempt at goal, although Grant McCann's 35-yard drive was easily dealt with by Saints goalkeeper Kelvin Davis.
Saints not surprisingly were on top at the start of the second half and Adam Lallana fizzed a shot over from 12 yards before Lambert forced Jones into a save.
Jones came to his side's rescue again on the hour, keeping out Lambert's header from Frazer Richardson's cross.
Lambert lashed another effort wide before Peterborough briefly threatened when Tommy Rowe let fly from 25 yards but he failed to find the target and McCann's long-range shot was saved by Davis.
But Peterborough hauled themselves back into the game in the 76th minute when Sinclair, introduced early in the second half, pounced from 12 yards.
Steve De Ridder missed a chance to secure the points for Saints when he shot wide but it mattered not as the home side held on for a 19th successive home win in all competitions.
