It was a fourth home success in a row, but the pressure to keep winning at The Dell - already fierce - will increase further if Dave Jones's team continue to falter on the road. After the Middlesbrough match on Sunday, their next trip is to Coventry on Easter Monday, which is a date to be ringed on all those Hampshire Countryside calendars, along with the visits from Blackburn (17 April) and Everton in a potential epic on the last day of the season.
On their own tight little pitch in front of supportive capacity crowds, and with an attacking formation, Southampton have dropped only two points since November. Picking both Matt Le Tissier and Hassan Kachloul behind two strikers gives their opponents something to think about most of the time, though to be fair to Jones, it is easy to see that his suspect defence does not then get the protection it needs.
Although Le Tissier made one important goalline clearance on Saturday, his best friends would not claim tracking opposing midfielders as a strength, and Kachloul's weakness in the same area meant that for long periods West Ham were able to attack at will down his flank. Unfortunately, Ian Pearce, a big, strong centre-half, spent the second half playing there, his wild shot over the bar from six yards out the result of having such an obviously square peg in a round hole.
Marc Keller and Eyal Berkovic were also guilty of bad misses from close in. When Trevor Sinclair shot more accurately, Paul Jones made two excellent saves, Scott Hiley backing him up on the second occasion with a heroic clearance under pressure. "I can't believe we haven't taken anything from the game," lamented Harry Redknapp, the manager. "I couldn't fault the effort, but the final bit of quality in delivering the ball or hitting the back of the net was missing."
Good fortune was hiding, as well, when Southampton mounted their first attack in the 10th minute, at which point West Ham had already had four scoring opportunities. Kachloul's drive would have gone straight to Shaka Hislop, but Rio Ferdinand's unnecessary deflection deceived the cooler Shaka and slid inside his right-hand post.
Even if the Saints are granted some of that sort of luck on their travels in the next six weeks, staying up will still be devilishly difficult.
Goal: Kachloul (10) 1-0.
Southampton (4-4-2): Jones; Hiley, Lundekvam, Benali, Colleter; Oakley, Le Tissier (Ripley, 85), Marsden, Kachloul; Beattie, M Hughes. Substitutes not used: D Hughes, Bridge, Moss, Marshall (gk).
West Ham United (3-5-2): Hislop; Pearce, Ferdinand, Ruddock; Lomas, Lampard, Foe (Kitson, 71), Berkovic, Keller; Sinclair, Di Canio. Substitutes not used: Minto, Moncur, Potts, Forrest (gk).
Referee: D Gallagher (Banbury).
Man of the match: Jones.