Striker Glenn Murray scored a brace and Jose Izquierdo curled in a shot from outside the box to lift promoted Brighton to 10th in the standings, leaving West Ham in 17th just above the relegation zone.
The visitors went ahead through Eric Maxim Choupo-Moting but Pascal Gross equalised just before the break only for Kurt Zouma to head Stoke back in front moments later. Jose Izquierdo then levelled for Brighton on the hour to earn a deserved point.
This and more from the happenings in the world of football
Brighton and Hove Albion made sure of Premier League football next season with two games to spare after a Pascal Gross goal gave them a memorable 1-0 home win over Manchester United on Friday.
The 26-year-old trained at the Mordovia Arena in Saransk on Monday but his state of fitness was still unclear.
Valencia sign Kondogbia on loan from Inter
'I can't comment on speculation. I don't bet and I don't do the lottery - it's not my way'
It is too early to say who has got the best of the most frenetic transfer market.
Leicester City added another tale of remarkable success to an incredible year by reaching the last 16 of the Champions League in their debut season with a 2-1 victory over Club Bruges.
Harry Kane's 101st Premier League goal was the difference as Tottenham Hotspur earned a 1-0 win over Arsenal, to continue their fine recent form in north London derbies in front of a Premier League record crowd at Wembley on Saturday.
Manchester City displayed champions' swagger as they roared clear at the top with a 5-0 trouncing of Burnley but it was drama which engulfed their neighbours Manchester United and Jose Mourinho that dominated the Premier League agenda on Saturday.