Both sides played out 2-2 draws just before the international break, with the Saints rescuing a point against Newcastle United while West Ham were pegged back by Crystal Palace.
Match preview
Seemingly down and out heading into the last knockings of their clash with Newcastle, Southampton's efforts at St James' Park did not appear to be bearing fruit after Callum Wilson and Allan Saint-Maximin twice put the Magpies ahead either side of Mohamed Elyounoussi's equaliser.
However, in the fifth minute of second-half injury time, Adam Armstrong was felled by Jamaal Lascelles, giving dead-ball specialist James Ward-Prowse the opportunity to rescue a point for his side, and the Saints captain needed no second invitation to crash home the penalty.
Hasenhuttl paid tribute to his side's "belief" after taking a point from an encounter where they arguably should have collected all three - but almost failed to take home any - and a tally of two points from a possible nine sees them sit 13th in the rankings at this early stage.
Thrashing Newport County 8-0 in the EFL Cup may have sold the St Mary's faithful false hope heading back into the Premier League, where that recent draw with Newcastle stretched Southampton's winless run in the division to five matches, and they have now gone 14 games without a clean sheet in the league.
The Saints have already held Manchester United to a 1-1 draw in front of their own fans this season, though, and only one of their last six Premier League home matches has ended in defeat, although they must now pit their wits against one of the country's most inspired and in-form outfits.
Newcastle and Leicester City could not stop the rampant machine that is David Moyes's West Ham during the first two weeks of the season, but one certain Chelsea loanee took it upon himself to halt the Hammers' momentum just before international football took precedence.
Twice West Ham took the lead against Crystal Palace through Pablo Fornals and, of course, Michail Antonio, but twice they were pegged back by Conor Gallagher, whose 12-minute brace prevented Moyes's side from claiming a third win on the trot during a pulsating four-goal draw.
However, seven points from a possible nine - with a goals tally of 10, the joint-highest alongside champions Manchester City - has quickly seen West Ham rise to second in the table, only behind Tottenham Hotspur and their perfect start to the season.
The real challenges will soon present themselves for West Ham, though, as they kick off their Europa League campaign away from home against Dinamo Zagreb on Thursday night, and they have failed to keep a clean sheet in any of their last eight Premier League matches away from home.
West Ham's record against Southampton makes for positive reading, though, as they have won six and drawn one of their last seven meetings with the South Coast club, whose most recent victory in this fixture was a 3-2 win at St Mary's in August 2017.
Southampton Premier League form:
Southampton form (all competitions):
West Ham United Premier League form:
Team News
Southampton striker Shane Long tested positive for coronavirus during the international break, but he was unlikely to force his way in over Che Adams or Adam Armstrong either way.
Stuart Armstrong's calf problem prevented him from linking up with the Scotland squad, and he remains a doubt for Saturday, but Southampton have no other fitness concerns to deal with, barring long-term absentee Will Smallbone.
Moussa Djenepo produced a contender for miss of the season against Newcastle and was hooked after 58 minutes for Nathan Redmond, who will hope to impress from the first whistle here.
West Ham remain fortunate on the injury front - with Winston Reid the club's only occupant of the treatment room - but Kurt Zouma may not be ready for his debut just yet after international duties and personal issues.
As a result, Craig Dawson and Angelo Ogbonna will hold their places in defence for the time being, and it would be a surprise to see Moyes make any alterations from the side that played out a pulsating draw with Palace.
Another record is there to be broken for Michail Antonio this weekend, as the 31-year-old could become the first player ever to score and assist in four consecutive Premier League matches.
Southampton possible starting lineup:
McCarthy; Livramento, Stephens, Salisu, Walker-Peters; Elyounoussi, Ward-Prowse, Romeu, Djenepo; Adams, Armstrong
West Ham United possible starting lineup:
Fabianski; Coufal, Dawson, Ogbonna, Cresswell; Rice, Soucek; Bowen, Fornals, Benrahma; Antonio
We say: Southampton 1-2 West Ham United
West Ham do not do boring matches, and as impressive as they have been on the goalscoring front so far, their defensive frailties were exposed by Gallagher in gameweek three.
Southampton have been able to take several positives from an otherwise disappointing start to the season on paper, but they have struggled in this fixture down the years and may fall just short once again.