West Ham 0 Brighton and Hove Albion 3: Murray double piles pressure back on Bilic
Murray struck either side of an effort from club-record signing Jose Izquierdo as Brighton damaged the feeling of resurgence that one defeat in five top-flight matches had given West Ham.
Bilic's side produced an insipid display and could be in the relegation zone by the time they face fellow strugglers Crystal Palace next week, while Brighton moved into the top half courtesy of the three points.
Murray got the Seagulls off to a great start by heading home his first Premier League goal since earning Bournemouth a shock victory at Chelsea in December 2015.
He exploited some shoddy defending from Pedro Obiang and the midfielder, as well as goalkeeper Joe Hart, should have done more to stop Izquierdo opening his Brighton account in first-half stoppage time.
West Ham have never overturned a two-goal half-time deficit in the Premier League and - after being booed off by unsatisfied supporters - they did not look like ending that record at the 76th attempt, with Murray wrapping up the win from the penalty spot after Pablo Zabaleta's clumsy challenge in the box.
2 - Both of Glenn Murray's braces in the Premier League have been against West Ham (also February 2015 for Crystal Palace). Thorn. pic.twitter.com/50Ng2uC3TF
— OptaJoe (@OptaJoe) October 20, 2017
Obiang started in place of the suspended Andy Carroll and his loose marking enabled Murray to connect with Pascal Gross' brilliant dead-ball delivery and head beyond Hart in the 10th minute.
West Ham gradually became more adventurous but Lewis Dunk flung his body in the way of a shot from Winston Reid to deflect it out for a corner before a strike from Manuel Lanzini suffered the same fate before the half-hour mark.
Javier Hernandez had a shot blocked by Shane Duffy before dragging an ambitious cross-goal effort wide as half-time approached and it proved costly as Brighton doubled their lead in the second minute of stoppage time.
Hart did well to deny Murray a second but when Izquierdo cut inside Obiang and curled a shot to the top-right corner, the goalkeeper's touch was not enough to keep it out of the net.
Bilic sent Andre Ayew on for Cheikhou Kouyate for the second half but West Ham struggled to break down a Brighton side intent to hold onto their advantage.
The hosts did not give Mat Ryan cause for concern until midway through the second half when Lanzini's 25-yard free-kick bent just outside the post after a touch off the wall.
Murray failed to beat Hart at his near-post after Anthony Knockaert's dazzling run down the right, but he had his second in the 75th minute.
Zabaleta's lazy tackle on Murray led to a penalty which the striker slid straight down the middle to clinch an impressive victory for Brighton that will result in questions about Bilic's future resurfacing.