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
1. Rob Sanchez 6/10
No chance with the goal. Calm and composed as always and dealt well with anything that came his way. One indecisive moment in the second half but recovered well
2. Ben White 7/10
Always looked in control and enjoyed a good tussle with the tricky Fornals and also Antonio when he drifted into wide areas. Another solid game for Brighton
3. Adam Webster 7/10
Getting back to his best after his ankle injury. Covered the central position well in Dunk's absence and led the backline
4. Dan Burn 7/10
Back in his most comfortable position and looked all the better for it. Defended well and decent in possession