Marian Pahars scored the only goal to help Southampton record their first win of the season.
The winner came in the 72nd minute when Pahars was brought down by Everton defender David Weir, who was booked for protesting at the decision by referee Steve Bennett.
But while Everton had cause for complaint as Pahars tumbled theatrically, they had only themselves to blame for at least drawing.
Everton had seven clear scoring chances and forced a total of 13 corners but was still unable to beat goalkeeper Paul Jones.
Jones made a succession of important saves from Tomasz Radzinski, Thomas Gravesen and Kevin Campbell.
But Weir, Radzinski and Campbell were all guilty of bad misses as Southampton clung on desperately at times.
In contrast Everton goalkeeper Paul Gerrard had little to do apart from turning around a long shot from Rory Delap and then saving at the foot of the same player.
Kent referee Bennett had a busy night and in the 26th minute acted on the advice of his fourth official Steve Dunn in dismissing Southampton manager Gordon Strachan from the touchline.
Strachan had remonstrated with Dunn after the award of a free kick on the other side of the field against one of his players, Wayne Bridge.
Bennett gave Strachan a stern lecture before sending him to sit for the rest of the match in the directors' box.
Southampton brought on Pahars in the 55th minute and also introduced at the same time Russian international and former Everton winger Andrei Kanchelskis for his debut.
Kanchelskis struggled to make an impact in the time available to him as Southampton held on desperately at times to their victory.
Another player making his debut, Everton Chinese international defender Li Weifeng marred an otherwise impressive first appearance with an injury-time booking for dissent