Having bounced back from a 3-2 home defeat to Crystal Palace with a 2-0 Premier League win against Manchester United last weekend - a result that prompted the departure of former Goodison Park boss David Moyes - Everton remain a point adrift of fourth-placed Arsenal, who undoubtedly have the easier run-in.
Arsene Wenger's men are due to host Newcastle United on Monday and West Brom before ending the season at Norwich City, while Everton meet Manchester City and Hull City after Saturday's trip to Southampton.
That means Roberto Martinez's side can ill-afford a slip-up this weekend if they are to pip Arsenal to fourth.
One factor that could work in Everton's favour at St Mary's Stadium is that Southampton have little to play for as they close in on a top-half finish.
That lack of incentive could go some way to explaining Southampton's recent run of having won just one of their last five games in the league, but their home record against Everton will be cause for optimism.
The Merseysiders have failed to win in their last four visits to the south coast and have triumphed in just one of their last 12 matches against this weekend's hosts.
If Everton can break that duck at Southampton's current ground, they will win their fourth away league game in a row for the first time since December 1985, but Martinez knows it will not be a straightforward task.
"(In terms of) football concepts they're one of most attractive teams in the league," he said. "There's a bravery about the way they play. Young players have big roles.
"It shows you the incredible progress they've had. We know we're going to face a really difficult team but in our eyes it's another very important game to be as good as we can.
"It's going to be one of the biggest tests we'll face this season."
Jay Rodriguez's season is over for Southampton and Mauricio Pochettino's men have not found the net in two games since the striker picked up a knee ligament injury against Manchester City three weeks ago.
Everton, meanwhile, will be without Kevin Mirallas (groin) for the remainder of 2013-14 and Lacina Traore (hamstring) is another set to miss the club's remaining three fixtures.
The visitors' biggest blow is that Sylvain Distin (hamstring) is unavailable for selection, and Martinez is reluctant to risk fellow centre-back Phil Jagielka (hamstring), meaning John Stones and Antolin Alcaraz will likely be partnered at the back.
