Brighton took the lead in the first half as Neal Maupay scored his fifth goal of the season on 44 minutes.
West Ham improved after the break and levelled on 66 minutes thanks to a nice side-footed finish from Ben Johnson.
Lewis Dunk put Brighton back into the lead after the break but a 82nd minute header from Tomas Soucek saw West Ham share the spoils.
Brighton move up to 16th in the table on 13 points from 15 matches while West Ham are 10th with 22 points from 15.
Scroll down and click through to see how the Albion players rated out of 10
1. Robert Sanchez 6/10
No chance with the goals. Very little else to do against a limited West Ham attack. Looked confident in what he did and barring any major mishaps looks like Brighton's No 1 for the foreseeable
2. Ben White 6/10
Criticised by Gary Neville for the equalising goal but did little else wrong. Played at right back and once again showed his versatility to this Albion team.
3. Lewis Dunk 7/10
As always a strong presence in the Brighton rearguard and instrumental in Albion's performance. A nice finish for Albion's second and it should've been the winner
4. Adam Webster 6/10
Slotted in at centre back as Brighton reverted to a back four. Looked comfortable in central defence and always looked to break forward when he could,