The Kenyan struck after just three minutes, finding the net from all of 40 yards following a hashed clearance from goalkeeper Eldin Jakupovic.
The Saints threatened again throughout the game, but their missed opportunities were never punished by an insipid Hull performance.
Below, Sports Mole looks at what happened at the KC Stadium, and how it happened.
© Getty Images
On target: 1
On target: 3
Was the result fair?
Undoubtedly. Southampton hit the front after just three minutes and there was never a single moment in the game when they looked like relinquishing their lead. The margin of victory should have been far greater for Ronald Koeman's side, but another solid defensive display will comfort the Dutchman in spite of his misfiring forwards on the day.
Hull City's performance
The hosts did nowhere near enough to salvage anything from this game, a theory reflected in the fact that they could only muster one shot on target throughout the 90 minutes.
Manager Steve Bruce will be happy enough with the defensive side of his team's performance after restricting free-scoring Southampton to just the one goal - and even that was handed to them on a plate - but they lacked enough quality at the other end of the field to truly test their opponents.
Southampton went into the game with a question mark hanging over their ability to sustain their early-season heroics, and there was nothing to suggest from their performance today that they could not continue on in the same vein. It was another fine defensive performance which showed just why they have conceded just five times all season, but they were never tested as much as they should have been.
The travelling fans broke into a rendition of 'we're going to win the league' at various points throughout the encounter and, with just four points separating them and leaders Chelsea, these chants are becoming increasingly less tongue-in-cheek.
Sports Mole's man of the match
Toby Alderweireld: You could justify awarding the man of the match to any of Southampton's back four this afternoon, all of whom produced fine, disciplined performances in defence to render their goalkeeper Fraser Forster little more than a close-range spectator. However, Alderweireld was particularly impressive.
Hull looked at their most dangerous shortly after falling behind, and the Belgian centre-half was on hand to ensure that their brief spell ultimately proved fruitless with a number of important clearances and blocks.
Third-choice goalkeeper Jakupovic had staked his claim for the number-one shirt after decent performances against Arsenal and Liverpool in recent weeks. However, the 30-year-old might well have blown his shot at regular football for the Tigers following his third-minute error in the build-up to Wanyama's opener.
The Kenyan found the net from all of 40 yards after Jakupovic's hashed clearance landed at his feet. Wanyama still had it all to do, but unfortunately for him the goal will be remembered for Jakupovic's error rather than his brilliant finish.
Martin Atkinson only had to brandish one yellow card - to Mohammed Diame in stoppage time - in what proved a very quiet day at the office for him. He did face a couple of penalty appeals, but on each occasion he looked to have made the correct decision.
Hull City: The Tigers travel to Turf Moor to face Burnley - who remain winless - next Saturday.
Southampton: Koeman's side are also in action against newly-promoted opposition as Leicester City travel to St Mary's on Saturday afternoon.