Mauricio Pochettino's side dominated from the outset at St Mary's, with Fulham failing to muster a single shot in a first-half in which headers from Rickie Lambert and Jay Rodriguez put the hosts deservedly ahead.
Only Maarten Stekelenburg's fine form, the goal frame and bad luck prevented Saints racking up an even greater margin of victory, as they secured a sixth clean sheet of the campaign - a far cry from the 26 goals they had conceded at the same stage of last season.
Adam Lallana scored the equaliser at Old Trafford and was almost involved in another goal after five minutes on the south coast.
The Saints captain dispossessed dawdling Philippe Senderos and went onto test Stekelenburg, whose parry would have been slotted home by Morgan Schneiderlin was it not for Fernando Amorebieta's clearance off the line.
Lambert fired a tame effort straight at Stekelenburg as Saints' fine start continued, before Senderos reacted quickly to stop the England international putting Rodriguez through on goal.
Another deep cross, this time from Lallana, found Lambert, whose looping header back across the goal was nodded home by Rodriguez.
It was one of 14 shots** **Southampton managed in a dominant first half, with play continuing in the same direction after the restart for which Aaron Hughes replaced Riether.
More top news
Freezing conditions have caused 24 hours of cross-channel travel chaos - which is set to continue into tonight.
The icy conditions has put a strain on many services in the South, especially those that help the elderly.
School children in Hampshire are performing the story of Mary and Joseph using songs by Take That.