Roberto Martinez's Everton team played out a fantastic display of attacking finesse and solid defending as they put three goals past one last season's best defences.
Two first half goals from Romelu Lukaku gave Southampton a mountain to climb in the second half with attempts from the saints failing to provide much danger.
Ross Barkley finished the game off with a smart curling effort giving his side the three important points, this was a big result for a team that had an unimpressive away record last term and it will give Martinez's team a confidence boost going forward this term.
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Southampton had the better of the opening 15 minutes of play with wide deliveries proving challenging for the Everton centre-backs Phil Jagielka and John Stones but the stern defence holding.
Around the 20 minute mark Tim Howard made an intuitive save with his legs to keep out Saido Mane drilled effort.
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The Toffees made the most of their counter attack through the opening goal of game when Lukaku's head met an accurately flighted cross from fellow forward Kone on 22 minutes.
Six minutes after the goal Lukaku was involved again, this time the Belgian turning provider as Ross Barkley failed to convert his chance from the centre of the 18 yard box for a two goal lead.
But the Belgium striker was not done yet as he powered into the box to receive a pass from Barkley and calmly slot in his second of the afternoon past a helpless Maarten Stekelenberg in the Saints goal.
The second half brought less opportunity for an Everton side attempting to see out their two goal cushion with Ronald Koeman's team seeking to cut the Toffees lead.
The Merseyside team defended well as an attack lead through Mane pushed in vain for a goal that would see the game open up in the second half with substitute Jay Rodriguez failing to provide what was needed up front.
The first challenging effort for Howard came on 79 minutes as Mane found himself 25 yards out in space unleashing a shot that had the power but not the precision as it proved a simple catch for the American keeper.
The final nail in the coffin for the saints came on 84 minutes when Seamus Coleman laid a ball across to the left side of the saints box with Barkley using the outside of his foot to set up a curling shot perfectly placed within Stekelenberg's goal for the third and final goal that ended a miserable day for Southampton.
Martinez's side take the three points back up to Merseyside with a perfect display and a clean sheet, the result was needed with tough tests over the horizon meanwhile Koeman will be ruing the lack of firepower up top after this opening to the season.