The France midfielder scored twice following Mark Noble's first-half opener before Graziano Pelle got his first Premier League strike.
Mark Noble opened the scoring in the first half after a period of dominance from the hosts, with his shot deflecting in off Maya Yoshida, but the Frenchman curled in a reply just before halftime.
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The Tottenham target, who the Saints have steadfastly refused to sell this summer, then sealed all three points with 20 minutes to go when he flicked home James Ward-Prowse's cross.
|VIEW FROM UPTON PARK
|By Alex Young
All the smiles of last week are long gone for West Ham as Southampton, helmed by the hugely impressive Morgan Schneiderlin, recovered from an early setback to steamroll the hosts at Upton Park.
The Frenchman, who has made no secret of his desire to leave the club this summer, was the heartbeat of a very efficient display and hints at a promising season following a brutal exodus of first-team players earlier in the transfer window.
It's not all doom and gloom for West Ham, though, as new arrivals Mauro Zarate and Cheikhou Kouyate shone brightest but Sam Allardyce needs to find a place to accomodate new and old in his system as the likes of Ricardo Vaz Te and Carlton Cole were passengers for the majority.
Barcelona midfielder Alex Song was introduced to the home fans before kickoff, having agreed a season-long loan deal at Upton Park, but the Cameroon international saw his new side start slowly.
Southampton dominated possession and had the first sight of goal, with Dusan Tadic dragging a shot wide from the edge of the box inside the opening five minutes.
West Ham still looked to be suffering a hangover from its midweek penalty shootout loss to third-tier Sheffield United in the League Cup but, after Ricardo Vaz Te was brilliantly denied by Fraser Forster, they took the lead against the run of play in fortuitous fashion.
Schneiderlin meekly surrendered possession in midfield and Noble was the beneficiary, picking up the loose ball before unleashing a long-range strike that took a heavy deflection off Yoshida on its way past Forster in the 27th minute.
That made it four goals for the midfielder against Southampton in his past four visits to Upton Park.
Koeman's side responded well and Pelle threatened with a header that was cleared by the well-placed Aaron Cresswell but there was no stopping Schneiderlin's effort on the stroke of halftime. The Frenchman collected a free kick unmarked at the back post and, though his initial shot was blocked by Joey O'Brien, his curling follow-up nestled into the back of the net.
Shane Long tried his luck early in the second half but was brilliantly denied by Adrian as the goalkeeper dived to his left to tip a vicious effort past the post.
The Spaniard had to be alert again in the 52nd minute to keep out Tadic's dangerous attempt, with Pelle denied by an erroneous offside flag seven minutes later after heading home Ward-Prowse's delivery.
The visitors were not to be denied, though, and Schneiderlin took advantage of West Ham's confusion as the home side debated the awarding of a corner, the 24-year-old tapping in Ward-Prowse's assist from close range.
Pelle grabbed the third seven minutes from time when Adrian could only parry Clyne's cross as Southampton celebrated a first league win of the campaign in style.