Neither side covered themselves in defensive glory in the capital as errors at both ends led to an exciting climax.
It was the visitors that dominated the first 45 minutes, with Danny Welbeck lashing an effort past the post, before Neil Maupay edged them in front before the break.
Dan Burn’s low cross caused problems in the Hammers box and Maupay stay alert to fire past Lukasz Fabianksi.
David Moyes threw on Andriy Yarmolenko and Manuel Lanzini after the break and the pair combined superbly to set up Ben Johnson’s first ever senior goal for the club.
Yarmolenko’s clever ball released Lanzini inside the area and his cutback was cushioned home by Johnson.
But despite growing into the ascendency in the final 20, West Ham shot themselves in the foot, as Lewis Dunk hauled Brighton back in front.
Solly March’s whipped cross caught the Hammers defence fast asleep from a corner and Dunk wriggled free to blast home.
But in the spirit of the season Potter’s team returned the favour to Moyes with another defensive clanger as Tomas Soucek powered home for a point.
Full Time at the London Stadium it’s West Ham 2 Brighton 2