Glenn Murray hits the winner as Brighton & Hove Albion end five-game Premier League winless run against in-form West Ham
Murray's side-footed 25th-minute finish - his 99th for Albion - proved the difference as Brighton scored just a second league success this season and their first since beating Manchester United at home back in August.
Brighton were made to work hard for the victory but saw it through in the end, keeping a first clean sheet in all competitions this term.
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Hide AdCentre-half Fabian Balbuena and Austrian Marko Arnautovic both missed guilt-edged chances for the Hammers in the second half but Albion held out, moving up to 12th following the triumph.
Brighton made three changes from the team that were beaten at champions Manchester City last time out. Iranian Alireza Jahanbakhsh was handed his first Premier League start for the club while frontman Glenn Murray and captain Bruno returned in place of Jurgen Locadia, Yves Bissouma and Martin Montoya.
In-form Hammers, unbeaten in their previous three Premier League fixtures - winning two - were unchanged from the side that toppled Jose Mourinho's Manchester United last Saturday.
The match started at a fast tempo with both sides offering early warning shots without creating any clear-cut chances.
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Hide AdWinger Anthony Knockaert looked lively from the outset, causing West Ham full-back Arthur Masuaku some problems in the early exchanges.
Irons were carrying threats of their own and nearly went ahead from a well-worked set-piece after 13 minutes. Felipe Anderson cleverly picked out frontman Marko Arnautovic on the edge from a free-kick but his thunderous, goalbound volley was blocked by Murray.
The visitors' had just survived a scare with Solly March wasteful having got behind West Ham's backline when Brighton pounced on some sloppy play from Andriy Yarmolenko, going ahead after 25 minutes.
Superb work from midfielder Beram Kayal saw him dispossess Yarmolenko, continuing a run down the left, he was picked out by Knockaert before firing in a fine cross which found an unmarked Murray to side-foot home from all of six yards.
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Hide AdWest Ham offered a response after going behind, missing a decent opportunity to get level on the half-hour. Anderson's clever diagonal was met by an unmarked Pablo Zabalata whose fizzed ball found Arnautovic but his effort was superbly blocked by Bruno and Obiang's drove his stroke on the rebound into the ground which sailed just over.
The Irons saw a fair amount of the ball leading in to the break but Albion were comfortable and led 1-0 at half-time.
Brighton were nearly architects of their own downfall three minutes after the restart. A sliced clearance from goalkeeper Mat Ryan went straight to Yarmolenko, fortunately for Albion centre-half Lewis Dunk recovered things before the West Ham wideman went over under a challenge with a free-kick awarded.
Manuel Pellegrini's half-time team talk appeared to have worked as Albion had to weather an onslaught from the Hammers. Arnautovic fired straight at Ryan after 53 minutes then the Irons should have levelled five minutes later. Centre-half Fabian Balbuena wriggled clear of Murray in the box, only to somehow head wide Anderson's corner from four yards.
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Hide AdChris Hughton threw on Jose Izquiredo, making just his second Seagulls appearance of the season, 20 minutes from time and he had an immediate impact. Good work from the Colombian saw him lead an Albion attack which ended with a corner being forced. From the resulting corner, Knockaert's delivery was delicious but Murray's free header went just over after 73 minutes.
Frontman Murray, now just a goal shy of a century for Brighton, then glanced another header over minutes later as Hughton's team could have doubled their lead.
Albion continued their search for a killer second and they thought they had it two minutes from time. Izquierdo's cut in from the left and his deflected shot was parried by Lukasz Fabianski straight to substitute Jurgen Locadia who was on hand to slot home, though, his effort was ruled out for offside.
West Ham were now throwing men forward in search of an opener which they should have had a minute later. Lucas Perez worked some room down the left, pulled back for Arnautovic, only for the Austrian to fire over unmarked from six yards.
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Hide AdBrighton remained solid right until the final-whistle, clinching a first success in six Premier League matches.
BRIGHTON: Ryan; Bruno, Duffy, Dunk, Bong; Propper, Kayal; Jahanbakhsh, March, Knockaert; Murray. Subs: Button, Balogun, Bissouma (Propper, 80), Izquierdo (Jahanbakhsh, 70), Locadia (March, 85), Andone.
WEST HAM: Fabianski; Zabaleta, Balbuena, Diop, Masuaku; Noble, Rice, Obiang; Yarmolenko, Arnautovic, Anderson. Subs: Adrian, Cresswell, Snodgrass (Noble, 83), Ogbonna, Fredericks, Perez (Yarmolenko, 70), Antonio (Obiang, 58).