In a South Coast clash often bereft of ingenuity on both ends, a late Adam Armstrong strike proved decisive for a relieved Russell Martin, whose side also had some Aaron Ramsdale heroics to thank for a long-awaited three points.
Saturday's St Mary's affair well and truly followed the Southampton script; the possession-dominant Saints had as much as 90% of the ball in the first 10 minutes, albeit without making it count as far as attacking plays were concerned.
Everton sought to press the hosts into errors when possible and had a couple of promising moments in the final third through Iliman Ndiaye, but quality was severely lacking in both boxes during a tepid contest.
It took until the final five minutes of the first half for the game to spring into life - Cameron Archer finally had the Saints' first shot in the 40th minute - but the South Coast clash could only get better from an entertainment point of view in the second half.
Sean Dyche's side were not short of chances to take the lead, but they were met by an impenetrable force in Aaron Ramsdale, before Armstrong finished off a sweeping counter-attack to trigger St Mary's bedlam.
There would be another late gut punch for Everton, whose central figurehead Beto had a last-minute goal disallowed for offside following a tight VAR call, and Martin surely felt a mixture of both elation and relief at full time.
Southampton's first win of the campaign temporarily takes them off the bottom of the table, but they will go back down to 20th if Wolverhampton Wanderers beat Crystal Palace in the evening kickoff, while Everton languish in 16th and are four points clear of the relegation zone.
SOUTHAMPTON VS. EVERTON HIGHLIGHTS
Aaron Ramsdale save vs. Everton (67th min, Southampton 0-0 Everton)
That is exactly what Southampton paid the big bucks for! Michael Keane surely must think that his downward header is bound for the bottom corner, but Ramsdale somehow manages to claw the ball onto the post and the hosts survive.
Adam Armstrong goal vs. Everton (85th min, Southampton 1-0 Everton)
Tenth time lucky? Southampton are just a matter of minutes away from their first Premier League win of the season!
Barely a moment after Beto smashes the crossbar for the visitors, Martin's men charge down the other end of the field, and Armstrong is on hand to meet Yukinari Sugawara's cut-back and propel the hosts ahead!
Beto disallowed goal vs. Southampton (90+1 min, Southampton 1-0 Everton)
Beto was the last-minute hero in Everton's draw with Fulham last weekend, and the Toffees striker briefly thinks that he has repeated the trick, lashing home from a long ball over the top.
The linesman's flag stays down initially, but after a good few minutes deliberation from the guys at Stockley Park, his effort is chalked off and the Saints survive.
MAN OF THE MATCH - AARON RAMSDALE
He may have been brutally axed from Arsenal's first XI, but on his day, there are few better out-and-out shot-stoppers than Aaron Ramsdale in the Premier League, and he proved as such on Saturday.
The Englishman produced five crucial saves to keep Everton at bay - including that wonder intervention from Keane - as well as registering two high claims to keep a richly-deserved clean sheet.
SOUTHAMPTON VS. EVERTON MATCH STATS
Possession: Southampton 65%-35% Everton
Shots: Southampton 9-16 Everton
Shots on target: Southampton 2-5 Everton
Corners: Southampton 3-6 Everton
Fouls: Southampton 14-18 Everton
WHAT NEXT?
In their final fixture before the international break, Southampton head to Molineux to face fellow basement side Wolverhampton Wanderers on November 9, while Everton battle West Ham United away from home next Saturday at 3pm.