Javier Hernandez cancelled out Glenn Murray's early opener for the Seagulls, but long-range strikes from Jose Izquierdo and Pascal Gross ensured that Chris Hughton's team won their first match in the top flight since December 23.
West Ham had gone into the fixture on a six-match unbeaten run in the top flight, but David Moyes's team were second best for much of the match and now only stay above Brighton on goal difference.
Brighton dominated the opening stages on the South coast and deservedly went in front when Anthony Knockaert and Gross combined to set up Murray, who kept his composure to slot the ball into the bottom corner from inside the penalty area
Moments after the goal, Murray attempted an overhead kick from 16 yards out, which inevitably went off target, while Izquierdo started to get more involved as the game entered the second quarter.
Four minutes later, though, the Hammers were level. Hernandez started the move and, after being aided by a neat flick from Joao Mario, the Mexican deceived two defenders before lashing the ball into the top corner from 14 yards.
Brighton were still having their moments, but West Ham were creating the better chances with Mario and Byram both sending the ball off target from close range after two more deliveries from the excellent Cresswell.
The opening 13 minutes of the second half passed by without incident and there appeared little danger when Izquierdo retrieved the ball after West Ham had cleared a corner.
However, the Colombian switched the ball onto his right foot and found the far top corner from 25 yards out, with Hammers goalkeeper Adrian getting nowhere near the strike.
The response from West Ham failed to come and Brighton looked the more likely to add to their lead, with Murray and Gross both sending the ball off target from promising positions.
That third goal did arrive with 15 minutes left as Gross was given the chance to turn on the edge of the penalty area before firing the ball into the bottom corner from 20 yards out.
As the game ticked into the final 10 minutes, Brighton continued to press forward with Beram Kayal and Solly March both going close, but Hughton and his players were content to see out the remaining minutes and seal a potentially-crucial success in their quest to stay in the Premier League.
BRIGHTON & HOVE ALBION (4-5-1): Ryan; Schelotto, Duffy, Dunk, Bong; Knockaert (March 77'), Stephens, Propper, Gross (Kayal 83'), Izquierdo; Murray (Ulloa 72')
WEST HAM UNITED (3-4-2-1): Adrian; Collins, Ogbonna, Rice (Antonio 66'); Byram (Hugill 80'), Zabaleta, Noble, Cresswell; Kouyate, Mario; Hernandez