An intriguing contest that promised much ultimately failed to live up to the billing, as both sides cancelled each other out on a night when clear-cut chances were at a premium.
Brighton posed the greater threat in the final third as the game edged closer to full time, but West Ham held on to claim a valuable point on home soil and extend their unbeaten run to four matches.
David Moyes's men remain sixth in the Premier League table, five points behind London rival Tottenham Hotspur in fifth, while Roberto De Zerbi's side have climbed above Manchester United into seventh place, three points behind the Hammers.
The West Ham faithful had little to get excited about in the opening exchanges as Brighton controlled the majority of the contest with patient build-up play, but neither side registered a single shot inside the first 20 minutes.
Facundo Buonanotte was the first player to provide a minor threat on West Ham's goal with a left-footed strike from the edge of the area, but an unfortunate block from teammate Danny Welbeck took the venom out of the shot as it bounced towards Alphonse Areola.
Brighton's Jason Steele was then called into action to keep out two strikes at the other end, firstly tipping a poked effort from Jarrod Bowen onto the outside of the post - the West Ham forward was ruled offside in the build-up, though - before standing firm to keep out a decent volley from James Ward-Prowse.
As the contest gradually livened up in the latter stages of the first half, Areola clawed away a looping header from Welbeck before throwing himself at a close-range shot by Jack Hinshelwood. Said Benrahma then curled a right-footed shot narrowly wide of the post at the other end.
The best chance of the first half felt to Pascal Gross three minutes before the break, but the German could only direct his free-header from inside the six-yard box straight at Areola after meeting a perfectly-weighted cross from James Milner.
Brighton enjoyed the better passages of play in possession shortly after the interval, and Welbeck was presented with a decent opportunity to open the scoring on the 54-minute mark, but his side-footed strike from inside the area was well saved by Areola down to his left.
Areola was tested again just a few minutes later, this time by Joao Pedro following a brilliant driving run towards goal, but the Seagulls striker could only poke a tame effort straight at the West Ham goalkeeper.
At the other end, Tomas Soucek, fresh from signing a new contract with the Hammers, almost bundled an effort over the line, but he could only place his shot from close range narrowly wide.
As Brighton began to regularly probe in an around West Ham's box, De Zerbi opted to replace Welbeck with Evan Ferguson shortly after the hour mark, and the Irishman almost made an immediate impact, expertly flicking the ball over Edson Alvarez before fizzing a low strike just inches wide of Areola's left-hand post.
Brighton were then enforced into another change as Adam Webster picked up an injury, with the defender - set to join an already packed treatment room - replaced by midfielder Jakub Moder, as De Zerbi attempted to reshuffle his lineup and fill square holes with round pegs.
The Seagulls ended the second half strongly, though, and penned West Ham into their own half, with the lively introduction of substitute Adam Lallana complimenting the threat of Ferguson and creativity of Gross, who directed a header narrowly wide 10 minutes from time before failing to make contact with an inviting cross from Moder.
Another chance then fell to Moder, but he lacked composure when it mattered and fired a poor first-time strike high over the crossbar from around six yards out, much to the frustration of De Zerbi throwing himself about on the touchline.
Just a few minutes later, Areola produced a fine one-handed save low down to his right to keep out Lallana, who did brilliantly to create space and swivel before unleashing a powerful shot from the edge of the area.
While West Ham ultimately missed the creativity and flair of attacking duo Mohammed Kudus and Lucas Paqueta, the former now away on AFCON duty with Ghana and the latter ruled out through injury, Brighton also lacked their usual spark in the final third, but one positive De Zerbi and co could take away from the London Stadium was that they kept their first Premier League clean sheet of the season at the 20th time of asking.
Both clubs will now turn their attention to the FA Cup third round, with Brighton travelling to Stoke City on Saturday and West Ham welcoming Bristol City to the London Stadium on Sunday.