Duncan Ferguson punished the Saints for some slack marking when he scored with a free header after just 11 minutes. Nick Barmby swung over a deep corner from the right and Ferguson was left unchallenged as he rose to power in a downward header for his ninth goal of the season.
It was just the start Southampton, deep in relegation trouble, did not want, and things went from bad to worse when Gary Speed increased Everton's lead after 27 minutes.
Earl Barrett made a surging run down the right flank and played a low ball into the centre. Speed picked it up on the edge of the penalty area and gave himself space to slot it past Maik Taylor in the Southampton goal.
Graham Souness made two changes at half-time in an attempt to make a comeback. Robbie Slater replaced Francis Benali and Eyal Berkovitch made way for the striker Mike Evans, who came on for his debut after his pounds 500,000 move from Plymouth Argyle.
The double substitution had the required effect as Saints hauled themselves level with two goals in as many minutes. The first came after 59 minutes, Slater scoring his first goal on his 19th appearance for Southampton.
The Australian international exchanged passes with Egil Ostenstad in a neat build-up on the edge of the penalty area before blasting the ball past Southall. Then, after 61 minutes, Jason Dodd crossed from the right and the Everton defender Craig Short headed past the advancing Southall and into his own net.
Taylor kept Saints on terms after 65 minutes with an important save from a header by Barmby as Everton sprang back into life. Joe Royle, the Everton manager, then brought Graham Stuart on for Claus Thomsen, but he failed to end a dreadful run in which his team have now taken just 10 points from their last 42.
Southampton: Taylor; Dodd (Charlton, 70), Dryden, Lundekvam, Benali (Slater, 46), Van Gobbel, Magilton, Neilson, Le Tissier, Berkovitch (Evans, 46), Ostenstad. Substitutes not used: Maddison, Moss (gk).
Everton: Southall; Barrett, Phelan, Watson, Unsworth, Parkinson, Thomsen, (Stuart, 74), Short, Barmby (Branch, 81), Ferguson, Speed. Substitutes not used: Rideout, Hottiger, Speare (gk).
Referee: P Durkin (Portland).