It was a very tight first half but Brighton broke the deadlock with just six minutes remaining courtesy of Danny Welbeck’s 50th Premier League goal.
The England international calmly lifted the ball over Hammers goalkeeper Lukasz Fabianski after being slipped in by substitute Percy Tau.
The lead was short-lived as West Ham substitute Said Benrahma swiftly levelled with his first goal for the club.
West Ham remain in the running for a European place while Brighton turn their attention to Tuesday night against Man City at the Amex.
Scroll down and click through to see who shone and who struggled for Brighton
5. AJ 7/10
Looked the most likely of all the Brighton attackers to make something happen. Good on the ball and looks fit and strong. replaced by Tau on 73.
6. Yves Bissouma 6/10
Made his mark in the first half with a crunching challnge on Lingard. He was then booked for a late challenge on Lingard but remained disciplined in the second half
7. Pascal Gross 6/10
Captain for the day in Dunk's absence. Pressed well in midfield and always look to pick that telling pass. Didn't see enough of the ball in the final third
8. Jakub Moder 6/10
A solid if unspectacular display. Always looking to run in behind and stretch the West Ham defence