Captain Phil Jagielka again led by example and scored the game’s only goal, Tim Howard made two outstanding saves to keep Southampton out and James McCarthy excelled in a more forward midfield role.
But in their absence, the futures of injured duo Romelu Lukaku and Darron Gibson took centre stage at Goodison Park.
Gibson’s appears more straight-forward, even if the length of time he will spend on the sidelines with a fractured bone in his foot is still to be confirmed.
The midfielder’s wretched luck with injuries struck again in training on Friday when he sustained what Everton described as a “small fracture to the fifth metatarsal.”
Gibson, only just fully recovered from a long-term knee injury that kept him out for the best part of a year ahead of a further three-month absence earlier this season, was looking to prove his fitness following a stomach muscle injury that forced him to miss Ireland’s European Championship qualifying draw with Poland last week.
But the former Manchester United man, 27, who had been influential in Everton’s two previous victories, is now awaiting a verdict from a specialist to see how long he will be missing this time.
If he avoids the need for surgery, he may make it back in six weeks, just before the season’s end and might therefore be available for Ireland’s crucial Euro 2016 qualifier against Scotland on 13 June.
If an operation is required that could be it until next season.
“It is disappointing and very unfair,” said Everton manager Roberto Martinez. “Darron had to work extremely hard from a long-term injury, the cruciate ligament injury he sustained a long time ago, and now I thought he was back at a very good level.
“It’s such a tough period. We need to support him and make sure we get him back as quick as we can.”
Top scorer Lukaku also missed the win over Southampton, which prevented the Saints from climbing above Liverpool into fifth place in the Premier League, with a hamstring injury but getting him fit again may be the least of Everton’s worries.
Their record signing from Chelsea has signed up Mino Raiola — whose clientele includes Zlatan Ibrahimovic, Mario Balotelli and Paul Pogba — as his new agent and already transfer talk has surfaced linking the striker with a possible summer move away from Merseyside just 12 months into a five-year contract.
“In the modern game you don’t get the values of 25 years ago. But when you have a player on a long-term contract there is nothing to discuss. That is straightforward and clear,” claimed Martinez.
“It is not as if the player wants to leave or that he is not happy.
“Since January he has been in terrific form.”
Without Lukaku, Everton didn’t pose a great attacking threat but once Jagielka had swept home his fifth goal of the season following a 15th-minute corner they didn’t need to.
Howard superbly denied both Graziano Pelle, now without a Premier League goal in 14 games, and James Ward-Prowse before half-time but even manager Ronald Koeman admitted his side lacked creativity after the break as their chances of a top-four finish looked to be finally extinguished.
The Dutchman added: “Everybody has got difficult games but it is not realistic at this moment to think of the first four positions.
“It is more realistic to think about the Europa League, but the Europa League for us is like the Champions League for Arsenal and Manchester United.”
Howard 8; Coleman 7, Stones 7, Jagielka 8, Baines 7; Barry 7; Lennon 7, McCarthy 8, Barkley 7 (Besic 70, 6), Osman 6; Kone 6 (Naismith 70, 6).
Davis 6; Clyne 7, Fonte 7, Alderweireld 7 (Duricic, 82), Bertrand 7; Wanyama 6, Schneiderlin 6; Long 6, Ward-Prowse 7 (Mane 61, 5), Elia 6 (Tadic 61, 7); Pelle 6.
Lee Mason 8