Southampton beat Barnsley at Oakwell to extend their club record winning run to eight league games.
Striker David Connolly capitalised on poor defending and hesitant goalkeeping to score with a close-range header.
Late on, Saints substitute Richard Chaplow was sent off for a studs-up and waist-high challenge on Jay McEveley.
Saints keeper Kelvin Davis twice saved well from Ricardo Vaz Te in injury time, while Miles Addison's effort was cleared off the line.
The result means Keith Hill's Barnsley side are yet to score a goal or win a game this season, while newly promoted Southampton are top and it is the first time they have won their opening two league games for 23 years.
Much of the Saints' good work came through Adam Lallana, who was drifting in from the right wing to great effect.
The visitors should have put the game beyond doubt with eight minutes to go, but Lallana's scuffed effort failed to test Preece.
Two minutes later Chaplow was dismissed, but Saints held on.