In sharp contrast, Brighton make the trip to the London Stadium having collected four points from fixtures with Manchester United and Newcastle United.
Match preview
Losing back-to-back fixtures to Manchester City and Nottingham Forest is not what David Moyes would have had in mind when thinking about his team's start to the season.
Nevertheless, the Hammers were unfortunate not to claim at least a point from the latter of those matches, and they have since posted a welcome 3-1 victory over Viborg FF in the Europa Conference League.
While West Ham desperately require points on the board in the top flight, Moyes will feel that his side are heading into the direction ahead of facing one of the in-form teams in the division.
Gianluca Scamacca netted his first goal since his big-money arrival from Sassuolo in midweek, the Italian now regarded as strong competition for long-term frontman Michail Antonio.
The addition of another defender in Thilo Kehrer has been equally as important, as has the long-awaited return of Angelo Ogbonna who got 65 minutes under his belt on Thursday after a serious knee injury.
As far as Brighton are concerned, Graham Potter will want to keep the ball rolling after his side came through their opening games with widespread credit.
Potter would have been disappointed with failing to take one of numerous opportunities during the goalless draw with Newcastle last weekend, but there was little wrong with his team's performance.
Consistency has always been Brighton's problem in the top flight, and that is something that will need to be addressed if they are to make the transition into a side who can challenge for the European places.
Although the Seagulls only claimed ninth position last season due to the capitulation of other teams, everything appears to be in place to contend higher up the table if they can solve their issues in front of goal.
While speculation persists that star midfielder Moises Caicedo is being targeted by the likes of Manchester United and Arsenal, Potter will insist on no more sales given the funds that have already been recouped for Yves Bissouma and Marc Cucurella and the money which is expected to be received for Neal Maupay over the coming days.
West Ham United Premier League form:
West Ham United form (all competitions):
Brighton & Hove Albion Premier League form:
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Even though Scamacca scored on his full debut in midweek, Antonio is expected to be recalled to the attack for this contest.
Goalkeeper Lukasz Fabianski should return between the sticks, while Kurt Zouma, Aaron Cresswell, Declan Rice and Said Benrahma also stand to be named in the West Ham XI.
While Kehrer will be considered for a debut in the centre of defence, Ben Johnson is likely to retain his spot.
Pervis Estupinan is pushing for his Brighton debut at left wing-back after making the switch from Villarreal earlier this week.
However, Potter may see no reason to make any alterations to his Brighton starting lineup, with Leandro Trossard and Adam Lallana expected to remain in their current positions.
West Ham United possible starting lineup:
Fabianski; Coufal, Zouma, Johnson, Cresswell; Soucek, Rice, Fornals; Bowen, Antonio, Benrahma
Brighton & Hove Albion possible starting lineup:
Sanchez; Veltman, Dunk, Webster; March, Mac Allister, Caicedo, Trossard; Gross, Lallana; Welbeck
We say: West Ham United 1-1 Brighton & Hove Albion
While Moyes would have been grateful to witness his team get a win under their belts in midweek, it meant that less focus has been placed on this fixture. With that in mind, we feel that Brighton will do more than enough to earn a share of the spoils in the capital.