Palmer turned in Marc Cucurella’s cross with a powerful header in the 34th minute to claim the 22nd league goal of his outstanding debut season and put the visitors in front at the Amex Stadium.

Nkunku side-footed home Malo Gusto’s pinpoint low cutback in the 64th minute to double Chelsea’s lead but they lost substitute Reece James to a straight red card for a petulant kick out at Joao Pedro in the 88th minute.

Danny Welbeck latched on to Pedro’s cross to snatch a goal back for the hosts in the seventh minute of stoppage time and ensure a frenetic end to the match.

Victory sent Chelsea into their final match against Bournemouth on Sunday with hope still alive of qualifying for the Europa League, despite a horrendous start to their campaign. Brighton, who are 10th, end the season at home to Manchester United.