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A first-minute goal from Charlie Austin proved the difference between the teams on Everton manager Ronald Koeman's return St Mary's Stadium.
Southampton manager Claude Puel handed a debut to 19-year-old debutant Josh Sims and he was immediately at the heart of the action, first having a shot blocked, then crossing for Austin to nod in after just 41 seconds.
Everton struggled for fluency before the break, while Sims caused them plenty of problems on the right wing.
Yannick Bolasie had a couple of shots after the break as Everton searched for the equaliser, while Romelu Lukaku went close with a free-kick.
Maarten Steklenburg pulled off a brilliant save from an Austin header with half an hour to go, then did superbly to deny James Ward-Prowse, and Puel was thrilled to see Southampton hold firm for their first win in five in the Premier League.
See: Southampton report | Everton report
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