Slaven Bilic's side were desperate to make amends for recent defeats against Watford and West Brom, but they were unable to produce their best form and failed to take anything from the game.
With another home game to come against Middlesbrough next weekend, Bilic will be hoping his side can get back on the winning trail and turn their season around.
It was a bright opening for the home side as they looked to start the game strongly and they could have opened the scoring after three minutes when Simone Zaza fired a shot past the post.
Zaza then turned provider on nine minutes as he laid the ball off for Michail Antonio who drilled a shot wide of the goal.
The Hammers continued to create the best openings and had claims for a penalty turned down on 15 minutes after Zaza appeared to be clipped in the box by Cedric but referee Jonathan Moss waved for play to continue.
Southampton made West Ham pay for those missed opportunities when they broke the deadlock on 40 minutes.
Dusan Tadic picked out Ryan Bertrand who cut the ball back for Austin and he beat Ogbonna to fire a left-foot shot past Adrian into the corner of the net.
The Hammers keeper came to West Ham's rescue two minutes later when he made a fine save to keep out a low shot from Nathan Redmond.
Adrian produced another fine save on 51 minutes when he produced a superb one handed save to keep out a low shot from Tadic.
But he could do nothing to stop Southampton adding a second on 62 minutes.
Austin turned provider this time as he played the perfect pass in for Tadic who took the ball around Adrian and slotted the ball into the back of the net.
The Hammers had strong claims once again for a penalty turned down on 72 minutes when Bertrand appeared to block substitute Sofiane Feghouli's shot with his hand, but Moss once again refused to point to the penalty spot.
West Ham refused to lie down and did their best to find a way back into the game.
Michail Antonio picked out Payet on the edge of the box and he stuck his shot inches past the post.
Saints defender Virgil Virgil van Dijk was then in the right place at the right time on 77 minutes to clear Zaza's effort off the line.
Southampton completed the victory in injury time when Steven Davis cut the ball back for Ward-Prowse and he fired the ball home from close-range.
With five defeats from the opening six Premier League games, Bilic will be doing everything this week to address the situation and will hope to find a winning formula against Middlesbrough next weekend.
West Ham: Adrian; Nordveit (Fletcher 71), Ogobnna, Reid, Arbeloa; Noble (Fernandes 82); Antonio, Kouyate, Lanzini (Feghouli 46), Payet; Zaza
Subs not used: Randolph, Byram, Obiang, Oxford
Bookings: Noble, Zaza, Reid, Payet
Southampton: Forster; Cedric (Martina 88), Van Dijk, Fonte, Bertrand; Romeu, Hojbjerg, Davis, Tadic (Ward-Prowse 80); Redmond, Austin (Long 74)
Subs not used: McCarthy, Yoshida, Clasie, Hesketh
Bookings: Romeu, Van Dijk
Referee: Jonathan Moss
Attendance: 56,864