Both teams have enjoyed fine starts to the season and were looking to claim three points before the international break.
Here, Sports Mole takes a closer look at the events that unfolded at St Mary's Stadium.
On Target 7
On Target 2
Was the result fair?
Southampton deserved to win today's game and produced some fantastic football, as their dream start to the season continued. They were a constant threat all afternoon and they could well have scored more than the four goals they netted. The visitors were poor from the start and could not handle their opponent's attacking threat. They were second best all over the pitch and their manager will agree that his side were not good enough.
The Saints were convincing from the start and it's no wonder that three of their players received call-ups to the England squad this week. Lambert and Lallana were the pick of their players and constantly provided a threat that the visitors could not cope with. Southampton's win moved them up to third place in the Premier League table, and based on today's performance, they more than deserve the plaudits that have come their way.
Hull City's performance
Hull have started the season well, but they were outplayed all afternoon by an impressive Southampton team. From the moment Schneiderlin scored, they never looked like getting back into the game. They briefly had a chance to mount a comeback when Yannick Sagbo scored, but if Steve Bruce's team are to stand any chance of staying in the league, they need to tighten up at the back and offer more of a threat in the final third.
Sports Mole's man of the match
Adam Lallana The midfielder was on top of his game today and scored one of the goals of the season to show that his place in the England squad is fully deserved. After winning the penalty that Lambert converted which make it 2-0, he added their third of the afternoon in truly remarkable circumstances. Lallana weaved his way through the Hull defence before keeping his composure and calmly finished past Steve Harper, to give Southampton an unassailable lead. If he continues to produce displays like he did today, then a place in the England squad for next year's World Cup is within his grasp.
With the Saints cruising and 3-0 up, Victor Wanyama almost ruined the good work his team had put in by gifting Hull a goal. He lost possession on the edge of the box to Sagbo, who made no mistake with his strike. Minutes later he was taken off, with his manager Mauricio Pochettino clearly angered and luckily for Wanyama, his mistake did not cost Southampton the three points.
Phil Dowd was in charge today and he got the game's big decision correct. The referee was right to give a penalty after Harper had brought down Lallana inside the box, with the keeper receiving a deserved yellow card for the foul. Dowd handed out two further bookings and on each occasion he got the decision spot on.
Southampton: The Saints face league leaders Arsenal at the Emirates Stadium on 23 November.
Hull City: City are next in action when they travel to Crystal Palace on 23 November.