Brighton edged ahead of Burnley thanks to a point at the London Stadium, but will be disappointed to have thrown away the chance of just a second win in 14 games.
Twice the Seagulls led as Neal Maupay's predatory finish to a loose ball inside the area just before half-time was just reward for Brighton's more purposeful approach in the first-half.
David Moyes reacted with two changes at half-time to liven up West Ham after a dire first 45 minutes and got the reaction he wanted when substitutes Andriy Yarmolenko and Manuel Lanzini teed up 20-year-old Ben Johnson for his first senior goal.
The visitors retook the lead when a corner broke perfectly for captain Lewis Dunk to fire high into the roof of the net.
However, Brighton's struggles at defending set-pieces cost them all three points when Tomas Soucek's header levelled eight minutes from time.