Swansea, beaten for the first time since Francesco Guidolin's appointment as head coach, remain 16th but are now only three points above the bottom three.
They visit Tottenham Hotspur and Arsenal in their next two games.
Unbeaten in their previous four matches, Swansea fielded an unchanged side, with South Korea midfielder Ki Sung-Yueng returning to the bench after missing the 1-1 draw at home to Crystal Palace with concussion.
Southampton attacking stats
Southampton recalled four players, among them fit-again pair Matt Targett and Steven Davis, and procured an early sight of goal when Graziano Pelle shot straight at Lukasz Fabianski from the edge of the box.
Swansea replied with a tame Andre Ayew effort, but the first half did not come to life until the verge of half-time, when the teams exchanged good chances in the space of a minute.
First, Gylfi Sigurdsson volleyed over for Swansea from Alberto Paloschi's flick-on, before the unmarked Long headed straight at Fabianski at the other end.
Pelle thought he had given Southampton the lead just before the hour when he turned the ball in after Fabianski had dropped it under pressure from Jose Fonte, but referee Jon Moss ruled that the Pole had been fouled.
However, 11 minutes later the visitors did go ahead as Long headed home an inviting cross from Ward-Prowse.
- Telegraph