The Hammers had not beaten the Seagulls since their promotion to the Premier League – a run that spanned six years and 12 games.
However, goals from James Ward-Prowse – his first for the Irons and 50th in the Premier League – Jarrod Bowen and Michail Antonio secured a fine victory for David Moyes’ side.
Alphonse Areola was in inspired form for the Hammers but was finally beaten when Pascal Gross found the corner with an inch perfect strike from outside the box, with ten minutes remaining.
Evan Ferguson and Lewis Dunk went close in injury-time but it was too little, too late for Albion, who were a shadow of the side that dismantled Wolves and Luton.
Here’s how Roberto De Zerbi’s players rated:
1. Brighton 1-3 West Ham
West Ham put on a counter attacking masterclass as they recorded their first ever Premier League victory over a below-par Brighton. Photo: Henry Browne/Getty Images
2. Bart Verbruggen - 5
Not the way he would have wanted his first Premier League game to go. Made a few comfortable saves but couldn't stop any of the goals. In fairness, he wasn't really helped by his defenders Photo: Charlie Crowhurst/Getty Images
3. James Milner - 5
Looked a bit leggy in the first half and struggled to keep up with West Ham's pacey attackers. Involved in a heated exchange, showing he's still got that fire in his belly. Looking to make an impact going forward. Good effort saved as Albion looked to fight back from three goal down Photo: Charlie Crowhurst/Getty Images
4. Lewis Dunk - 6
Not his best game for Brighton but was among the better performers on the pitch. Was too casual in certain moments. Two cracking headers kept out by an inspired Alphonse Areola and another cleared off the line by a defender. Photo: Henry Browne/Getty Images