The France striker's 64th-minute strike on Thursday (AEST) added to Cole Palmer's 22nd goal of the campaign in the 34th minute at Amex Stadium as Chelsea claimed their fourth straight victory to boost ambitions of qualifying for a European competition next season.
Chelsea moved three points behind fifth-placed Tottenham heading into the final round of games in the league on Sunday, while Manchester United kept alive their hopes of playing in Europe by beating Newcastle United 3-2.
Nkunku, a signature signing from Leipzig in the last off-season, has endured an injury-hit first year at Stamford Bridge and has managed just 10 league appearances, scoring three goals. His latest was a close-range finish from Malo Gusto's cross.
Palmer, another signing last year, has been Chelsea's shining light and glanced in a header from Marc Cucurella's left-wing cross to leave him five goals behind Erling Haaland's league-leading tally of 27.
Second-half substitute Reece James was shown a straight red card in the 88th — following a VAR review — after he kicked out at Joao Pedro while on the ground.
"Maybe it's the frustration of him," Chelsea manager Mauricio Pochettino said.
"... It was a fantastic night of football and he's our captain and a really important player.
"I'm disappointed because now he's going to miss the next game and maybe a few games in next season."
Danny Welbeck grabbed the Seagulls' consolation goal in the seventh minute of added time.
Kobbie Mainoo gets Manchester United on the scoreboard in the win over Newcastle United. (AP PHOTO)
At Old Trafford, a strike by substitute Rasmus Hojlund in the 84th minute proved the difference as under-pressure Dutch manager Erik ten Hag gained a much-needed victory in his team's last home game of the season.
The hosts joined the seventh-placed Magpies on 57 points but have an inferior goal difference.
The teams finishing in sixth and seventh should qualify for the Europa League and Europa Conference League, respectively. The Red Devils could also get in the Europa League by winning the FA Cup final against Manchester City on May 25.
Ten Hag, who thanked fans for their support after the game and promised to "give everything" to win the Wembley Stadium derby said: "I don't talk about pride - we are all disappointed with the season - but still, we can win something and we have to go for this."
Kobbie Mainoo put Manchester United ahead in the 31st after a pass was slipped through the Newcastle defence by Amad Diallo, who regained the lead for the home side with a fierce left-footed shot after a 57th-minute corner wasn't fully cleared.
Anthony Gordon had equalised in the 49th and Lewis Hall ensured a nervy finish to the game for by making it 3-2 in added time.
With PA.
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