With the top seven realistically out of reach for Brighton, a potential route to the UEFA Conference League via eighth place was their only practical motive to turn on the style today.
However, West Ham could have stunned them inside 10 minutes when Tomas Soucek could only ripple the side netting despite being unmarked inside the area.
In true footballing fashion, they were punished for that miss – and ‘punished’ in some style too, as Yasin Ayari curled home a goal of the season contender from 30 yards.
After a frantic opening 15 minutes, a lull followed, although the Seagulls did have to survive a brief VAR scare when Mohammed Kudus tumbled in the area.
And there was an even bigger scare for them soon after, when Soucek rose highest in the area to head goalwards, but a stunning fingertip save from Bart Verbruggen kept them ahead.
The South coast side could perhaps count themselves a little unlucky not to have taken a two-goal lead a few minutes before the break, as they put the ball in the back of the net for a second time, this time via Simon Adingra - but a swift VAR check confirmed Mats Wieffer had strayed offside in the build up.
They were left to rue that disallowed goal within five minutes of the restart. Jarrod Bowen did the legwork in the build-up.
Weaving his way to the byline, he executed a cut back that somehow evaded no fewer than five Brighton defenders before being swept into the corner by Kudus.
That leveller spurred the Hammers into life, and they came close to hitting the front through the unlikely source of Aaron Wan-Bissaka, but his ferocious strike was repelled at the near post by Verbruggen.
Jack Hinshelwood did come close to nosing Brighton back in front, but his deflected effort dropped just the right side of the post for those of a West Ham persuasion.
Things got even better for them in the closing stages, when Bowen was once again the provider, floating a perfect cross onto the head of Soucek, who powered home at the far post to secure what seemed to be West Ham’s first away league win whilst conceding in over a year.
But old habits die hard for Potter’s side, and they surrendered their lead in the dying moments when Kaoru Mitoma was left unmarked six yards out and he had the simplest of tasks to head home Brajan Gruda’s knockdown.
A draw did little to help Brighton, though, and in probing for a late winner, they found one in added time, when Carlos Baleba popped up to curl home from 35 yards, netting what could be a huge goal for their European ambitions.
Flashscore Man of the Match: Brajan Gruda (Brighton & Hove Albion)