Bournemouth up to third after sinking Saints
Eddie Howe's side took control in the local derby at St Mary's thanks to first half goals from Nathan Ake and Harry Wilson.
James Ward-Prowse's penalty reduced the deficit after half-time, but Bournemouth survived a late barrage of pressure before Callum Wilson sealed their third league win this season.
It was Bournemouth's first ever win at Southampton at the 16th attempt.
"That's a very nice feeling at this early stage but that's all it is. We need to keep grounded," Howe said of Bournemouth's top four spot.
"We rarely get those moments in football where you get that pure emotion and joy for a few seconds. Then you start thinking about next week!
"There were some heroics from our goalkeeper. You want the players brought down to earth because you want the focus on consistent success."
Southampton remain in mid-table after losing for the third time in their opening six games.
The hosts went close early on when Cedric Soares crossed to Ward-Prowse and he poked wide from close-range.
But it was Bournemouth who took the lead in the 10th minute when former Chelsea defender Ake rose above a crowd of defenders to power a header past Angus Gunn from Diego Rico's corner.
Seven of Ake's last eight Premier League goals have been scored from corners.
Josh King thought he had doubled Bournemouth's lead in the 25th minute when the striker took Dominic Solanke's pass and slotted home.
However, with the Bournemouth celebrations well under way, a VAR review ruled out the goal as King had one foot in an offside position.
It was only as temporary reprieve for Southampton as Howe's men struck again in the 35th minute.
King and Philip Billing carved open the Saints defence with a swift exchange of passes, leaving Wilson to slot into the bottom corner for the on-loan Liverpool midfielder's third goal of the season.
Southampton were in desperate need of a quick response and when Nathan Redmond's cut-back fell for Pierre-Emile Hojbjerg, his close-range effort was repelled by Cherries keeper Aaron Ramsdale, who also produced another fine save to keep out Redmond's drive.
Southampton were jeered off at half-time, but they were back in it in the 53rd minute.
Che Adams was brought down by Steve Cook's clumsy challenge in the penalty area and Ward-Prowse stepped up to drill the spot-kick past Ramsdale.
King's bad luck with VAR continued when he had a penalty appeal turned down after being bundled over by Cedric.
Sofiane Boufal shot straight at Ramsdale and Redmond's goalbound strike was blocked by Jack Stacey as Southampton pressed in vain for an equaliser.
Ramsdale saved well from Danny Ings before Wilson was gifted the third goal deep into stoppage-time when he tapped into the empty net after a mix-up between Gunn and Jan Bednarek.